Continuous limit is discrete

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bahman
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Continuous limit is discrete

Post by bahman »

What exists is the continuous limit where the limit is considered to becoming as close as possible to a specific point but never reaching the point. This means that what we call it continuous limit is discrete.
Age
Posts: 20194
Joined: Sun Aug 05, 2018 8:17 am

Re: Continuous limit is discrete

Post by Age »

bahman wrote: Tue Feb 23, 2021 8:16 pm What exists is the continuous limit where the limit is considered to becoming as close as possible to a specific point but never reaching the point. This means that what we call it continuous limit is discrete.
The main reason you say 'it' never reaches 'that point' is just because you see, consider, and say 'that point' is a 'separate', 'discrete' 'point'.

And, contrary to "bahman's" BELIEF, obviously what "bahman" sees, considers, and says is absolutely and irrefutably true, right, and correct is NOT necessarily true, right, nor correct at all. Unless, of course, "bahman" can PROVE what "it" says is true, right, and correct IS actually True, Right, and Correct. What can be CLEARLY SEEN here is that there is NO 'proof' AT ALL in those two sentences, provided so far.

So, either PROVE what you CLAIM is TRUE, or just ACCEPT that it might NOT be true AT ALL.
Dimebag
Posts: 520
Joined: Sun Mar 06, 2011 2:12 am

Re: Continuous limit is discrete

Post by Dimebag »

bahman wrote: Tue Feb 23, 2021 8:16 pm What exists is the continuous limit where the limit is considered to becoming as close as possible to a specific point but never reaching the point. This means that what we call it continuous limit is discrete.
A few definitions first.
continuous
/kənˈtɪnjʊəs/
See definitions in:
All
Mathematics
Grammar
adjective
1.
forming an unbroken whole; without interruption.
"the whole performance is enacted in one continuous movement"
Similar:
continual
uninterrupted
unbroken
constant
ceaseless
limit
/ˈlɪmɪt/
See definitions in:
All
Motoring
Alcoholic
Mathematics
noun
1.
a point or level beyond which something does not or may not extend or pass.
"the failure showed the limits of British power"
2.
a restriction on the size or amount of something permissible or possible.
"an age limit"
discrete
/dɪˈskriːt/
adjective
individually separate and distinct.
"speech sounds are produced as a continuous sound signal rather than discrete units"
Similar:
separate
distinct
individual
detached
unattached
disconnected
discontinuous
Now, the descriptions of continuous and discrete are mutually exclusive. Continuous being unbroken, whole. Essentially, something continuous could in theory be artificially or arbitrarily divided an infinite number of times and points. Something discrete is inherently already divided, segmented, pixelated and has clear boundaries between divisions.

Now, I am not sure how the addition of a limit, being a point or boundary beyond which something can not pass, to something continuous, makes it now discrete? What parts of something continuous with a limit are discrete? Surely before the limit, the continuous section is, as described, continuous NOT discrete. Now, if you want to put a limit on both ends of this continuous “thing” maybe then you can treat it AS one single discrete “thing”, but then, by implication, all discrete parts are continuous. I’m not sure that is true. So, the treating of a limited and bound continuous thing as something discrete would seem an artificial case of something discrete, not truly discrete.

Discrete would imply also, having the SAME value through the WHOLE of that segment. Something continuous obviously is constantly changing, throughout its “length”, and thus, does not possess the same characteristics of something discrete.

I think it’s best to treat discrete things as discrete, and continuous things as continuous, and, limited continuous things, as just that. Sound fine?
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bahman
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Re: Continuous limit is discrete

Post by bahman »

Age wrote: Fri Feb 26, 2021 9:11 am
bahman wrote: Tue Feb 23, 2021 8:16 pm What exists is the continuous limit where the limit is considered to becoming as close as possible to a specific point but never reaching the point. This means that what we call it continuous limit is discrete.
The main reason you say 'it' never reaches 'that point' is just because you see, consider, and say 'that point' is a 'separate', 'discrete' 'point'.
No, it is by definition of the continuous limit. The limit is as it is defined as when you get close to the point but never reach it. There is a reason behind that though. You cannot have any motion if you reach the point. You for example cannot calculate the derivative.
Age wrote: Fri Feb 26, 2021 9:11 am And, contrary to "bahman's" BELIEF, obviously what "bahman" sees, considers, and says is absolutely and irrefutably true, right, and correct is NOT necessarily true, right, nor correct at all. Unless, of course, "bahman" can PROVE what "it" says is true, right, and correct IS actually True, Right, and Correct. What can be CLEARLY SEEN here is that there is NO 'proof' AT ALL in those two sentences, provided so far.

So, either PROVE what you CLAIM is TRUE, or just ACCEPT that it might NOT be true AT ALL.
The definition of motion/speed for example is V=dx/dt=limit DX/Dt where Dt tends to zero. You get V=0/0 if you set DT=0 since Dx=0 also that is problematic since 0/0 is undefined. That is why people define the limit as Dt to be very small but never zero.
User avatar
bahman
Posts: 8791
Joined: Fri Aug 05, 2016 3:52 pm

Re: Continuous limit is discrete

Post by bahman »

Dimebag wrote: Fri Feb 26, 2021 12:16 pm
bahman wrote: Tue Feb 23, 2021 8:16 pm What exists is the continuous limit where the limit is considered to becoming as close as possible to a specific point but never reaching the point. This means that what we call it continuous limit is discrete.
A few definitions first.
continuous
/kənˈtɪnjʊəs/
See definitions in:
All
Mathematics
Grammar
adjective
1.
forming an unbroken whole; without interruption.
"the whole performance is enacted in one continuous movement"
Similar:
continual
uninterrupted
unbroken
constant
ceaseless
limit
/ˈlɪmɪt/
See definitions in:
All
Motoring
Alcoholic
Mathematics
noun
1.
a point or level beyond which something does not or may not extend or pass.
"the failure showed the limits of British power"
2.
a restriction on the size or amount of something permissible or possible.
"an age limit"
discrete
/dɪˈskriːt/
adjective
individually separate and distinct.
"speech sounds are produced as a continuous sound signal rather than discrete units"
Similar:
separate
distinct
individual
detached
unattached
disconnected
discontinuous
Now, the descriptions of continuous and discrete are mutually exclusive. Continuous being unbroken, whole. Essentially, something continuous could in theory be artificially or arbitrarily divided an infinite number of times and points. Something discrete is inherently already divided, segmented, pixelated and has clear boundaries between divisions.

Now, I am not sure how the addition of a limit, being a point or boundary beyond which something can not pass, to something continuous, makes it now discrete? What parts of something continuous with a limit are discrete? Surely before the limit, the continuous section is, as described, continuous NOT discrete. Now, if you want to put a limit on both ends of this continuous “thing” maybe then you can treat it AS one single discrete “thing”, but then, by implication, all discrete parts are continuous. I’m not sure that is true. So, the treating of a limited and bound continuous thing as something discrete would seem an artificial case of something discrete, not truly discrete.

Discrete would imply also, having the SAME value through the WHOLE of that segment. Something continuous obviously is constantly changing, throughout its “length”, and thus, does not possess the same characteristics of something discrete.

I think it’s best to treat discrete things as discrete, and continuous things as continuous, and, limited continuous things, as just that. Sound fine?
Let's focus on the definition of motion/speed for example which is given by V=limit Dx/Dt when Dt tends to zero. Dt is a positive nonzero quantity in here. We can get close to the real value of V by making Dt as small as possible but we can never set it zero since we are dealing with 0/0 which is undefined.
Dimebag
Posts: 520
Joined: Sun Mar 06, 2011 2:12 am

Re: Continuous limit is discrete

Post by Dimebag »

bahman wrote: Fri Feb 26, 2021 3:56 pm
Dimebag wrote: Fri Feb 26, 2021 12:16 pm
bahman wrote: Tue Feb 23, 2021 8:16 pm What exists is the continuous limit where the limit is considered to becoming as close as possible to a specific point but never reaching the point. This means that what we call it continuous limit is discrete.
A few definitions first.
continuous
/kənˈtɪnjʊəs/
See definitions in:
All
Mathematics
Grammar
adjective
1.
forming an unbroken whole; without interruption.
"the whole performance is enacted in one continuous movement"
Similar:
continual
uninterrupted
unbroken
constant
ceaseless
limit
/ˈlɪmɪt/
See definitions in:
All
Motoring
Alcoholic
Mathematics
noun
1.
a point or level beyond which something does not or may not extend or pass.
"the failure showed the limits of British power"
2.
a restriction on the size or amount of something permissible or possible.
"an age limit"
discrete
/dɪˈskriːt/
adjective
individually separate and distinct.
"speech sounds are produced as a continuous sound signal rather than discrete units"
Similar:
separate
distinct
individual
detached
unattached
disconnected
discontinuous
Now, the descriptions of continuous and discrete are mutually exclusive. Continuous being unbroken, whole. Essentially, something continuous could in theory be artificially or arbitrarily divided an infinite number of times and points. Something discrete is inherently already divided, segmented, pixelated and has clear boundaries between divisions.

Now, I am not sure how the addition of a limit, being a point or boundary beyond which something can not pass, to something continuous, makes it now discrete? What parts of something continuous with a limit are discrete? Surely before the limit, the continuous section is, as described, continuous NOT discrete. Now, if you want to put a limit on both ends of this continuous “thing” maybe then you can treat it AS one single discrete “thing”, but then, by implication, all discrete parts are continuous. I’m not sure that is true. So, the treating of a limited and bound continuous thing as something discrete would seem an artificial case of something discrete, not truly discrete.

Discrete would imply also, having the SAME value through the WHOLE of that segment. Something continuous obviously is constantly changing, throughout its “length”, and thus, does not possess the same characteristics of something discrete.

I think it’s best to treat discrete things as discrete, and continuous things as continuous, and, limited continuous things, as just that. Sound fine?
Let's focus on the definition of motion/speed for example which is given by V=limit Dx/Dt when Dt tends to zero. Dt is a positive nonzero quantity in here. We can get close to the real value of V by making Dt as small as possible but we can never set it zero since we are dealing with 0/0 which is undefined.
You will have to explain yourself here a little more.

As I understand it, v=dx/dt is an equation for finding a velocity of something. As such dx is the difference in distance of the thing in question travelling over difference in the time period t.

The “real” value of v is simply going the be the value which is calculated from whatever distance and time is covered in that particular case. Adjusting t close to 0 is then changing things such that x will also necessarily change, because the relationship between v, x and t are all covarying.

At any rate, please continue and expand, explaining your reasoning such that a child could interpret your explanation. Do not assume that placing an equation for velocity and playing with things a bit makes your point, this is philosophy where your points need to make logical coherent sense, such that ANYONE could follow the logic you profess, and come to the SAME conclusion.

Thanks.
Age
Posts: 20194
Joined: Sun Aug 05, 2018 8:17 am

Re: Continuous limit is discrete

Post by Age »

bahman wrote: Fri Feb 26, 2021 3:49 pm
Age wrote: Fri Feb 26, 2021 9:11 am
bahman wrote: Tue Feb 23, 2021 8:16 pm What exists is the continuous limit where the limit is considered to becoming as close as possible to a specific point but never reaching the point. This means that what we call it continuous limit is discrete.
The main reason you say 'it' never reaches 'that point' is just because you see, consider, and say 'that point' is a 'separate', 'discrete' 'point'.
No, it is by definition of the continuous limit.
So, what you are essentially saying here is; you express a word, or more, provide them with your very own, very specific definitions, and then use those, not to be found anywhere else, definitions to then claim that what you are seeing and saying is true, is irrefutably true, correct?

Also, are you saying there is actually a continuation, but it actually stops at some limited point?

If this is what you are saying, then 'where', EXACTLY, is this "point"?

But if that is not what you are saying, then what are you actually saying?
bahman wrote: Fri Feb 26, 2021 3:49 pm The limit is as it is defined as when you get close to the point but never reach it.
But is this, (imagined?), "point" in imagination only or in 'actuality'?

If it exists in 'actuality', then 'where' AND 'when', EXACTLY?
bahman wrote: Fri Feb 26, 2021 3:49 pm There is a reason behind that though.
There is a reason behind 'what' though?

I really wish you would not write in a way where I am expected to ASSUME things.
bahman wrote: Fri Feb 26, 2021 3:49 pmYou cannot have any motion if you reach the point.
Of course NOT. This goes WITHOUT saying. But, also, relatively when one is at that 'point', then are still 'in motion'. As there can NOT be a 'thing', which is NOT 'in motion', and thus NOT 'changing'.
bahman wrote: Fri Feb 26, 2021 3:49 pm You for example cannot calculate the derivative.
I could NOT care less.

I just LOOK AT and EXPRESS 'that' what IS actually True, ONLY.

I do NOT 'need to' nor even want to 'look to' forming calculations in order to 'try to' verify, nor falsify, what "others" have 'theorized' or 'claimed' is true.
bahman wrote: Fri Feb 26, 2021 3:49 pm
Age wrote: Fri Feb 26, 2021 9:11 am And, contrary to "bahman's" BELIEF, obviously what "bahman" sees, considers, and says is absolutely and irrefutably true, right, and correct is NOT necessarily true, right, nor correct at all. Unless, of course, "bahman" can PROVE what "it" says is true, right, and correct IS actually True, Right, and Correct. What can be CLEARLY SEEN here is that there is NO 'proof' AT ALL in those two sentences, provided so far.

So, either PROVE what you CLAIM is TRUE, or just ACCEPT that it might NOT be true AT ALL.
The definition of motion/speed for example is V=dx/dt=limit DX/Dt where Dt tends to zero.
But that is NOT a 'definition' AT ALL of 'motion/speed'. They are just some symbols used in mathematical formulas, of which the majority of human beings have absolutely NO clue NOR idea AT ALL of what they mean or are actually referring to. And nearly EVERY one of that MAJORITY of human beings have absolutely NO interest AT ALL in what those symbols mean or are referring to.

If you would like some 'real life' examples of DEFINITIONS, for the words 'motion' and 'speed', then I will provide you with some.

'Motion', the action or process of moving or being moved; a formal proposal put to a legislature or committee.

'Speed', the rate at which someone or something moves or operates or is able to move or operate; move quickly.

Also, there are other actual DEFINITIONS for these two words if you are Truly interested in seeing them?
bahman wrote: Fri Feb 26, 2021 3:49 pm You get V=0/0 if you set DT=0 since Dx=0 also that is problematic since 0/0 is undefined. That is why people define the limit as Dt to be very small but never zero.
But ABSOLUTELY NOTHING of this refers to the FACT that you CLAIMED there is a "continuation" with a "limit", which you ONLY said because there is absolutely NOTHING in the WHOLE Universe that could PROVE your CLAIM true about there being 'discrete', in relation to 'motion' and/or 'duration'.

As I have CLEARLY POINTED out earlier, while a human being has a BELIEF, then they will say just about ANY 'thing', in order to back up and support that BELIEF, which they can NOT back up and support with ACTUAL EVIDENCE nor PROOF.

You "bahman" are just PROVIDING another PRIME EXAMPLE of this ABSURD BEHAVIOR here.
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bahman
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Re: Continuous limit is discrete

Post by bahman »

Dimebag wrote: Fri Feb 26, 2021 9:20 pm
bahman wrote: Fri Feb 26, 2021 3:56 pm
Dimebag wrote: Fri Feb 26, 2021 12:16 pm

A few definitions first.







Now, the descriptions of continuous and discrete are mutually exclusive. Continuous being unbroken, whole. Essentially, something continuous could in theory be artificially or arbitrarily divided an infinite number of times and points. Something discrete is inherently already divided, segmented, pixelated and has clear boundaries between divisions.

Now, I am not sure how the addition of a limit, being a point or boundary beyond which something can not pass, to something continuous, makes it now discrete? What parts of something continuous with a limit are discrete? Surely before the limit, the continuous section is, as described, continuous NOT discrete. Now, if you want to put a limit on both ends of this continuous “thing” maybe then you can treat it AS one single discrete “thing”, but then, by implication, all discrete parts are continuous. I’m not sure that is true. So, the treating of a limited and bound continuous thing as something discrete would seem an artificial case of something discrete, not truly discrete.

Discrete would imply also, having the SAME value through the WHOLE of that segment. Something continuous obviously is constantly changing, throughout its “length”, and thus, does not possess the same characteristics of something discrete.

I think it’s best to treat discrete things as discrete, and continuous things as continuous, and, limited continuous things, as just that. Sound fine?
Let's focus on the definition of motion/speed for example which is given by V=limit Dx/Dt when Dt tends to zero. Dt is a positive nonzero quantity in here. We can get close to the real value of V by making Dt as small as possible but we can never set it zero since we are dealing with 0/0 which is undefined.
You will have to explain yourself here a little more.

As I understand it, v=dx/dt is an equation for finding a velocity of something. As such dx is the difference in distance of the thing in question travelling over difference in the time period dt.
The bold part is the correction.
Dimebag wrote: Fri Feb 26, 2021 12:16 pm The “real” value of v is simply going the be the value which is calculated from whatever distance and time is covered in that particular case. Adjusting t close to 0 is then changing things such that x will also necessarily change, because the relationship between v, x and t are all covarying.
x is a function of t that is mathematically represented as x=x(t). Velocity v is the first derivative of x.
Dimebag wrote: Fri Feb 26, 2021 12:16 pm At any rate, please continue and expand, explaining your reasoning such that a child could interpret your explanation. Do not assume that placing an equation for velocity and playing with things a bit makes your point, this is philosophy where your points need to make logical coherent sense, such that ANYONE could follow the logic you profess, and come to the SAME conclusion.

Thanks.
We might be able to calculate the first derivative if we know x(t) analytically assuming that Dt is small enough. This however requires some tricks which mathematicians come with the excellent ones to calculate the first derivative of many functions. For example, these are tricks that are used to calculate the first derivative of trigonometric functions. Such tricks are not available for all functions. Therefore, we cannot calculate the first derivative precisely and analytically. In simple words, we cannot know what is dx/dt=0/0 in this case which is the continuous regime. We can however do approximation considering that dx is finite but very small.
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bahman
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Joined: Fri Aug 05, 2016 3:52 pm

Re: Continuous limit is discrete

Post by bahman »

Age wrote: Fri Feb 26, 2021 11:54 pm
bahman wrote: Fri Feb 26, 2021 3:49 pm
Age wrote: Fri Feb 26, 2021 9:11 am
The main reason you say 'it' never reaches 'that point' is just because you see, consider, and say 'that point' is a 'separate', 'discrete' 'point'.
No, it is by definition of the continuous limit.
So, what you are essentially saying here is; you express a word, or more, provide them with your very own, very specific definitions, and then use those, not to be found anywhere else, definitions to then claim that what you are seeing and saying is true, is irrefutably true, correct?

Also, are you saying there is actually a continuation, but it actually stops at some limited point?

If this is what you are saying, then 'where', EXACTLY, is this "point"?

But if that is not what you are saying, then what are you actually saying?
bahman wrote: Fri Feb 26, 2021 3:49 pm The limit is as it is defined as when you get close to the point but never reach it.
But is this, (imagined?), "point" in imagination only or in 'actuality'?

If it exists in 'actuality', then 'where' AND 'when', EXACTLY?
bahman wrote: Fri Feb 26, 2021 3:49 pm There is a reason behind that though.
There is a reason behind 'what' though?

I really wish you would not write in a way where I am expected to ASSUME things.
bahman wrote: Fri Feb 26, 2021 3:49 pmYou cannot have any motion if you reach the point.
Of course NOT. This goes WITHOUT saying. But, also, relatively when one is at that 'point', then are still 'in motion'. As there can NOT be a 'thing', which is NOT 'in motion', and thus NOT 'changing'.
bahman wrote: Fri Feb 26, 2021 3:49 pm You for example cannot calculate the derivative.
I could NOT care less.

I just LOOK AT and EXPRESS 'that' what IS actually True, ONLY.

I do NOT 'need to' nor even want to 'look to' forming calculations in order to 'try to' verify, nor falsify, what "others" have 'theorized' or 'claimed' is true.
bahman wrote: Fri Feb 26, 2021 3:49 pm
Age wrote: Fri Feb 26, 2021 9:11 am And, contrary to "bahman's" BELIEF, obviously what "bahman" sees, considers, and says is absolutely and irrefutably true, right, and correct is NOT necessarily true, right, nor correct at all. Unless, of course, "bahman" can PROVE what "it" says is true, right, and correct IS actually True, Right, and Correct. What can be CLEARLY SEEN here is that there is NO 'proof' AT ALL in those two sentences, provided so far.

So, either PROVE what you CLAIM is TRUE, or just ACCEPT that it might NOT be true AT ALL.
The definition of motion/speed for example is V=dx/dt=limit DX/Dt where Dt tends to zero.
But that is NOT a 'definition' AT ALL of 'motion/speed'. They are just some symbols used in mathematical formulas, of which the majority of human beings have absolutely NO clue NOR idea AT ALL of what they mean or are actually referring to. And nearly EVERY one of that MAJORITY of human beings have absolutely NO interest AT ALL in what those symbols mean or are referring to.

If you would like some 'real life' examples of DEFINITIONS, for the words 'motion' and 'speed', then I will provide you with some.

'Motion', the action or process of moving or being moved; a formal proposal put to a legislature or committee.

'Speed', the rate at which someone or something moves or operates or is able to move or operate; move quickly.

Also, there are other actual DEFINITIONS for these two words if you are Truly interested in seeing them?
bahman wrote: Fri Feb 26, 2021 3:49 pm You get V=0/0 if you set DT=0 since Dx=0 also that is problematic since 0/0 is undefined. That is why people define the limit as Dt to be very small but never zero.
But ABSOLUTELY NOTHING of this refers to the FACT that you CLAIMED there is a "continuation" with a "limit", which you ONLY said because there is absolutely NOTHING in the WHOLE Universe that could PROVE your CLAIM true about there being 'discrete', in relation to 'motion' and/or 'duration'.

As I have CLEARLY POINTED out earlier, while a human being has a BELIEF, then they will say just about ANY 'thing', in order to back up and support that BELIEF, which they can NOT back up and support with ACTUAL EVIDENCE nor PROOF.

You "bahman" are just PROVIDING another PRIME EXAMPLE of this ABSURD BEHAVIOR here.
All I am saying is that 0/0 has a problem. It is undefined. So velocity is not defined in the continuous limit. Please see this thread.
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bahman
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Re: Continuous limit is discrete

Post by bahman »

Dimebag wrote: Fri Feb 26, 2021 9:20 pm
bahman wrote: Fri Feb 26, 2021 3:56 pm
Dimebag wrote: Fri Feb 26, 2021 12:16 pm

A few definitions first.







Now, the descriptions of continuous and discrete are mutually exclusive. Continuous being unbroken, whole. Essentially, something continuous could in theory be artificially or arbitrarily divided an infinite number of times and points. Something discrete is inherently already divided, segmented, pixelated and has clear boundaries between divisions.

Now, I am not sure how the addition of a limit, being a point or boundary beyond which something can not pass, to something continuous, makes it now discrete? What parts of something continuous with a limit are discrete? Surely before the limit, the continuous section is, as described, continuous NOT discrete. Now, if you want to put a limit on both ends of this continuous “thing” maybe then you can treat it AS one single discrete “thing”, but then, by implication, all discrete parts are continuous. I’m not sure that is true. So, the treating of a limited and bound continuous thing as something discrete would seem an artificial case of something discrete, not truly discrete.

Discrete would imply also, having the SAME value through the WHOLE of that segment. Something continuous obviously is constantly changing, throughout its “length”, and thus, does not possess the same characteristics of something discrete.

I think it’s best to treat discrete things as discrete, and continuous things as continuous, and, limited continuous things, as just that. Sound fine?
Let's focus on the definition of motion/speed for example which is given by V=limit Dx/Dt when Dt tends to zero. Dt is a positive nonzero quantity in here. We can get close to the real value of V by making Dt as small as possible but we can never set it zero since we are dealing with 0/0 which is undefined.
You will have to explain yourself here a little more.

As I understand it, v=dx/dt is an equation for finding a velocity of something. As such dx is the difference in distance of the thing in question travelling over difference in the time period t.

The “real” value of v is simply going the be the value which is calculated from whatever distance and time is covered in that particular case. Adjusting t close to 0 is then changing things such that x will also necessarily change, because the relationship between v, x and t are all covarying.

At any rate, please continue and expand, explaining your reasoning such that a child could interpret your explanation. Do not assume that placing an equation for velocity and playing with things a bit makes your point, this is philosophy where your points need to make logical coherent sense, such that ANYONE could follow the logic you profess, and come to the SAME conclusion.

Thanks.
Also please read this thread.
Age
Posts: 20194
Joined: Sun Aug 05, 2018 8:17 am

Re: Continuous limit is discrete

Post by Age »

bahman wrote: Sat Feb 27, 2021 1:11 am
Age wrote: Fri Feb 26, 2021 11:54 pm
bahman wrote: Fri Feb 26, 2021 3:49 pm
No, it is by definition of the continuous limit.
So, what you are essentially saying here is; you express a word, or more, provide them with your very own, very specific definitions, and then use those, not to be found anywhere else, definitions to then claim that what you are seeing and saying is true, is irrefutably true, correct?

Also, are you saying there is actually a continuation, but it actually stops at some limited point?

If this is what you are saying, then 'where', EXACTLY, is this "point"?

But if that is not what you are saying, then what are you actually saying?
bahman wrote: Fri Feb 26, 2021 3:49 pm The limit is as it is defined as when you get close to the point but never reach it.
But is this, (imagined?), "point" in imagination only or in 'actuality'?

If it exists in 'actuality', then 'where' AND 'when', EXACTLY?
bahman wrote: Fri Feb 26, 2021 3:49 pm There is a reason behind that though.
There is a reason behind 'what' though?

I really wish you would not write in a way where I am expected to ASSUME things.
bahman wrote: Fri Feb 26, 2021 3:49 pmYou cannot have any motion if you reach the point.
Of course NOT. This goes WITHOUT saying. But, also, relatively when one is at that 'point', then are still 'in motion'. As there can NOT be a 'thing', which is NOT 'in motion', and thus NOT 'changing'.
bahman wrote: Fri Feb 26, 2021 3:49 pm You for example cannot calculate the derivative.
I could NOT care less.

I just LOOK AT and EXPRESS 'that' what IS actually True, ONLY.

I do NOT 'need to' nor even want to 'look to' forming calculations in order to 'try to' verify, nor falsify, what "others" have 'theorized' or 'claimed' is true.
bahman wrote: Fri Feb 26, 2021 3:49 pm
The definition of motion/speed for example is V=dx/dt=limit DX/Dt where Dt tends to zero.
But that is NOT a 'definition' AT ALL of 'motion/speed'. They are just some symbols used in mathematical formulas, of which the majority of human beings have absolutely NO clue NOR idea AT ALL of what they mean or are actually referring to. And nearly EVERY one of that MAJORITY of human beings have absolutely NO interest AT ALL in what those symbols mean or are referring to.

If you would like some 'real life' examples of DEFINITIONS, for the words 'motion' and 'speed', then I will provide you with some.

'Motion', the action or process of moving or being moved; a formal proposal put to a legislature or committee.

'Speed', the rate at which someone or something moves or operates or is able to move or operate; move quickly.

Also, there are other actual DEFINITIONS for these two words if you are Truly interested in seeing them?
bahman wrote: Fri Feb 26, 2021 3:49 pm You get V=0/0 if you set DT=0 since Dx=0 also that is problematic since 0/0 is undefined. That is why people define the limit as Dt to be very small but never zero.
But ABSOLUTELY NOTHING of this refers to the FACT that you CLAIMED there is a "continuation" with a "limit", which you ONLY said because there is absolutely NOTHING in the WHOLE Universe that could PROVE your CLAIM true about there being 'discrete', in relation to 'motion' and/or 'duration'.

As I have CLEARLY POINTED out earlier, while a human being has a BELIEF, then they will say just about ANY 'thing', in order to back up and support that BELIEF, which they can NOT back up and support with ACTUAL EVIDENCE nor PROOF.

You "bahman" are just PROVIDING another PRIME EXAMPLE of this ABSURD BEHAVIOR here.
All I am saying is that 0/0 has a problem.
0/0, itself, does NOT have 'a problem'.

ONLY 'you', human beings, make and created 'problems'. Thus, it is ONLY 'you', human beings, who have 'a problem', here.
bahman wrote: Sat Feb 27, 2021 1:11 am It is undefined.
If 'it' is 'undefined', and 'this' causes 'you' a 'problem', a 'concern', or an 'issue', then I suggest that 'you' just go ahead and 'define' 'it'.
bahman wrote: Sat Feb 27, 2021 1:11 am So velocity is not defined in the continuous limit.
This is because there is NO actual 'discrete'. Which can be and will be PROVEN True.
bahman wrote: Sat Feb 27, 2021 1:11 am Please see this thread.
I saw 'that' thread.
Age
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Re: Continuous limit is discrete

Post by Age »

bahman wrote: Sat Feb 27, 2021 1:12 am
Dimebag wrote: Fri Feb 26, 2021 9:20 pm
bahman wrote: Fri Feb 26, 2021 3:56 pm
Let's focus on the definition of motion/speed for example which is given by V=limit Dx/Dt when Dt tends to zero. Dt is a positive nonzero quantity in here. We can get close to the real value of V by making Dt as small as possible but we can never set it zero since we are dealing with 0/0 which is undefined.
You will have to explain yourself here a little more.

As I understand it, v=dx/dt is an equation for finding a velocity of something. As such dx is the difference in distance of the thing in question travelling over difference in the time period t.

The “real” value of v is simply going the be the value which is calculated from whatever distance and time is covered in that particular case. Adjusting t close to 0 is then changing things such that x will also necessarily change, because the relationship between v, x and t are all covarying.

At any rate, please continue and expand, explaining your reasoning such that a child could interpret your explanation. Do not assume that placing an equation for velocity and playing with things a bit makes your point, this is philosophy where your points need to make logical coherent sense, such that ANYONE could follow the logic you profess, and come to the SAME conclusion.

Thanks.
Also please read this thread.
You appear to be puzzled by a lot of other things as well. But what do you propose 'us' reading that you admit to this will achieve?
Dimebag
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Re: Continuous limit is discrete

Post by Dimebag »

Bahman, I think I understand what you are attempting to explain. Basically, that if you divide a continuous function into small enough parts you might consider them to be discrete jumps. Yet, you know this can’t be the case. Discrete functions are cases where each individual coordinate is separate from each other point, yet, given the example of trying to find the derivative of a continuous function where t tends towards 0 but doesn’t approach, we know that difference in x and or t will always be connected to its adjacent section of the function.

You want to pixelate something continuous, but by nature, continuous mean it can be infinitely divided, meaning there are NO discrete individual points, only arbitrarily limited ones, which still share boundaries between neighboring ones. To try to find the derivative of single point on a function, as you mentioned, would result in 0/0, undefined. There must be change to find the derivative, or slope. Taking a snapshot of for example the movement of some object gives you no information about its tradjectory, without allowing some time to pass and observing its velocity, momentum etc.

I see what you are trying to do, but I don’t think you can.
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bahman
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Re: Continuous limit is discrete

Post by bahman »

Age wrote: Sat Feb 27, 2021 2:48 am
bahman wrote: Sat Feb 27, 2021 1:11 am
Age wrote: Fri Feb 26, 2021 11:54 pm

So, what you are essentially saying here is; you express a word, or more, provide them with your very own, very specific definitions, and then use those, not to be found anywhere else, definitions to then claim that what you are seeing and saying is true, is irrefutably true, correct?

Also, are you saying there is actually a continuation, but it actually stops at some limited point?

If this is what you are saying, then 'where', EXACTLY, is this "point"?

But if that is not what you are saying, then what are you actually saying?



But is this, (imagined?), "point" in imagination only or in 'actuality'?

If it exists in 'actuality', then 'where' AND 'when', EXACTLY?



There is a reason behind 'what' though?

I really wish you would not write in a way where I am expected to ASSUME things.



Of course NOT. This goes WITHOUT saying. But, also, relatively when one is at that 'point', then are still 'in motion'. As there can NOT be a 'thing', which is NOT 'in motion', and thus NOT 'changing'.



I could NOT care less.

I just LOOK AT and EXPRESS 'that' what IS actually True, ONLY.

I do NOT 'need to' nor even want to 'look to' forming calculations in order to 'try to' verify, nor falsify, what "others" have 'theorized' or 'claimed' is true.



But that is NOT a 'definition' AT ALL of 'motion/speed'. They are just some symbols used in mathematical formulas, of which the majority of human beings have absolutely NO clue NOR idea AT ALL of what they mean or are actually referring to. And nearly EVERY one of that MAJORITY of human beings have absolutely NO interest AT ALL in what those symbols mean or are referring to.

If you would like some 'real life' examples of DEFINITIONS, for the words 'motion' and 'speed', then I will provide you with some.

'Motion', the action or process of moving or being moved; a formal proposal put to a legislature or committee.

'Speed', the rate at which someone or something moves or operates or is able to move or operate; move quickly.

Also, there are other actual DEFINITIONS for these two words if you are Truly interested in seeing them?

But ABSOLUTELY NOTHING of this refers to the FACT that you CLAIMED there is a "continuation" with a "limit", which you ONLY said because there is absolutely NOTHING in the WHOLE Universe that could PROVE your CLAIM true about there being 'discrete', in relation to 'motion' and/or 'duration'.

As I have CLEARLY POINTED out earlier, while a human being has a BELIEF, then they will say just about ANY 'thing', in order to back up and support that BELIEF, which they can NOT back up and support with ACTUAL EVIDENCE nor PROOF.

You "bahman" are just PROVIDING another PRIME EXAMPLE of this ABSURD BEHAVIOR here.
All I am saying is that 0/0 has a problem.
0/0, itself, does NOT have 'a problem'.

ONLY 'you', human beings, make and created 'problems'. Thus, it is ONLY 'you', human beings, who have 'a problem', here.
0/0 has a problem since it could be any value as it is illustrated in another thread.
Age wrote: Sat Feb 27, 2021 2:48 am
bahman wrote: Sat Feb 27, 2021 1:11 am It is undefined.
If 'it' is 'undefined', and 'this' causes 'you' a 'problem', a 'concern', or an 'issue', then I suggest that 'you' just go ahead and 'define' 'it'.
0/0 has a mathematical problem so I cannot assign a number to it.
Age wrote: Sat Feb 27, 2021 2:48 am
bahman wrote: Sat Feb 27, 2021 1:11 am So velocity is not defined in the continuous limit.
This is because there is NO actual 'discrete'. Which can be and will be PROVEN True.
bahman wrote: Sat Feb 27, 2021 1:11 am Please see this thread.
I saw 'that' thread.
So what is your opinion? Did you see the problem of 0/0?
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Re: Continuous limit is discrete

Post by bahman »

Dimebag wrote: Sat Feb 27, 2021 1:04 pm Bahman, I think I understand what you are attempting to explain. Basically, that if you divide a continuous function into small enough parts you might consider them to be discrete jumps. Yet, you know this can’t be the case. Discrete functions are cases where each individual coordinate is separate from each other point, yet, given the example of trying to find the derivative of a continuous function where t tends towards 0 but doesn’t approach, we know that difference in x and or t will always be connected to its adjacent section of the function.

You want to pixelate something continuous, but by nature, continuous mean it can be infinitely divided, meaning there are NO discrete individual points, only arbitrarily limited ones, which still share boundaries between neighboring ones. To try to find the derivative of single point on a function, as you mentioned, would result in 0/0, undefined. There must be change to find the derivative, or slope. Taking a snapshot of for example the movement of some object gives you no information about its tradjectory, without allowing some time to pass and observing its velocity, momentum etc.

I see what you are trying to do, but I don’t think you can.
My problem is the derivative is defined as a limit and in the limit, you never reach the point while we are interested in the exact derivative of the function which means that we have to set dt equal to zero which is problematic. This means that although a continuous function is plausible but we have a problem with defining the derivative or continuous motion.
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