Philosophy Now Forum

That's because the expression as described is indeterminate which means y can be any number along with +/- infinity. If you don't believe me, check a book on calculus.

PhilX

Philosophy Explorer wrote:That's because the expression as described is indeterminate which means y can be any number along with +/- infinity. If you don't believe me, check a book on calculus.

PhilX

No, I don't believe you.

A_Seagull wrote:

Philosophy Explorer wrote:That's because the expression as described is indeterminate which means y can be any number along with +/- infinity. If you don't believe me, check a book on calculus.

PhilX

No, I don't believe you.

You're entitled.

PhilX

Philosophy Explorer wrote:

A_Seagull wrote:

Philosophy Explorer wrote:That's because the expression as described is indeterminate which means y can be any number along with +/- infinity. If you don't believe me, check a book on calculus.

PhilX

No, I don't believe you.

You're entitled.

PhilX

Thank you.

BTW Do you have any idea what you are talking about? Do you have any examples whereby 1^n doesn't equal 1?

A_Seagull wrote:Thank you.

BTW Do you have any idea what you are talking about? Do you have any examples whereby 1^n doesn't equal 1?

I sure do. For example let n = 1/2. This means the square root of 1. There will be two answers, 1 and -1 because their squares equal 1. If you continue (e.g. n = 1/4, 1/8, 1/16, etc.), you will produce two noncontinuous lines, one of them one unit above the x-axis, the other one unit below the x-axis. These lines are not continuous so as you let n get smaller, then technically speaking, y isn't approaching a limit but bounces back and forth between 1 and -1. This why this is described as being indeterminate since y alternates. Simple? (btw I'm slightly misleading in saying that y can take on any value. Nevertheless it is still an indeterminate form as you can't assign a single value to y and have a continuous line which is what I wanted to bring out).

PhilX

Philosophy Explorer wrote:

A_Seagull wrote:Thank you.

BTW Do you have any idea what you are talking about? Do you have any examples whereby 1^n doesn't equal 1?

I sure do. For example let n = 1/2. This means the square root of 1. There will be two answers, 1 and -1 because their squares equal 1. If you continue (e.g. n = 1/4, 1/8, 1/16, etc.), you will produce two noncontinuous lines, one of them one unit above the x-axis, the other one unit below the x-axis. These lines are not continuous so as you let n get smaller, then technically speaking, y isn't approaching a limit but bounces back and forth between 1 and -1. This why this is described as being indeterminate since y alternates. Simple? (btw I'm slightly misleading in saying that y can take on any value. Nevertheless it is still an indeterminate form as you can't assign a single value to y and have a continuous line which is what I wanted to bring out).

PhilX

So in essence what you are saying is that y=1^0.5 is indeterminate because there are two solutions?

If you were to argue that this could be a problem for logicians who want to insist that something either is or is not, with nothing in between, then I would agree with you. But it I snot a problem for mathematics.

A_Seagull wrote:

Philosophy Explorer wrote:

A_Seagull wrote:Thank you.

BTW Do you have any idea what you are talking about? Do you have any examples whereby 1^n doesn't equal 1?

I sure do. For example let n = 1/2. This means the square root of 1. There will be two answers, 1 and -1 because their squares equal 1. If you continue (e.g. n = 1/4, 1/8, 1/16, etc.), you will produce two noncontinuous lines, one of them one unit above the x-axis, the other one unit below the x-axis. These lines are not continuous so as you let n get smaller, then technically speaking, y isn't approaching a limit but bounces back and forth between 1 and -1. This why this is described as being indeterminate since y alternates. Simple? (btw I'm slightly misleading in saying that y can take on any value. Nevertheless it is still an indeterminate form as you can't assign a single value to y and have a continuous line which is what I wanted to bring out).

PhilX

So in essence what you are saying is that y=1^0.5 is indeterminate because there are two solutions?

If you were to argue that this could be a problem for logicians who want to insist that something either is or is not, with nothing in between, then I would agree with you. But it I snot a problem for mathematics.

Another way of putting it is it's not a function. Calculus loves functions.

PhilX

Philosophy Explorer wrote:

A_Seagull wrote:Thank you.

BTW Do you have any idea what you are talking about? Do you have any examples whereby 1^n doesn't equal 1?

I sure do. For example let n = 1/2. This means the square root of 1. There will be two answers, 1 and -1 because their squares equal 1. If you continue (e.g. n = 1/4, 1/8, 1/16, etc.), you will produce two noncontinuous lines, one of them one unit above the x-axis, the other one unit below the x-axis. These lines are not continuous so as you let n get smaller, then technically speaking, y isn't approaching a limit but bounces back and forth between 1 and -1. This why this is described as being indeterminate since y alternates. Simple? (btw I'm slightly misleading in saying that y can take on any value. Nevertheless it is still an indeterminate form as you can't assign a single value to y and have a continuous line which is what I wanted to bring out).

PhilX

So what, Phil? Is this a statement of deep truth or is it just a meaningless mathematical curiosity?

Obvious Leo wrote:

Philosophy Explorer wrote:

A_Seagull wrote:Thank you.

BTW Do you have any idea what you are talking about? Do you have any examples whereby 1^n doesn't equal 1?

I sure do. For example let n = 1/2. This means the square root of 1. There will be two answers, 1 and -1 because their squares equal 1. If you continue (e.g. n = 1/4, 1/8, 1/16, etc.), you will produce two noncontinuous lines, one of them one unit above the x-axis, the other one unit below the x-axis. These lines are not continuous so as you let n get smaller, then technically speaking, y isn't approaching a limit but bounces back and forth between 1 and -1. This why this is described as being indeterminate since y alternates. Simple? (btw I'm slightly misleading in saying that y can take on any value. Nevertheless it is still an indeterminate form as you can't assign a single value to y and have a continuous line which is what I wanted to bring out).

PhilX

So what, Phil? Is this a statement of deep truth or is it just a meaningless mathematical curiosity?

Meaningless to you. Meaningful to mathematicians.

PhilX

Philosophy Explorer wrote:Meaningless to you. Meaningful to mathematicians.

This is not an answer to my question. In what way is it meaningful?

Obvious Leo wrote:

Philosophy Explorer wrote:Meaningless to you. Meaningful to mathematicians.

This is not an answer to my question. In what way is it meaningful?

It's a case of a math expression that isn't a function. Do you know what a function is?

PhilX

Philosophy Explorer wrote:. Do you know what a function is?

Yes. A function is an event which is usually boring and at which inferior quality booze is dispensed in insufficient quantity.

Obvious Leo wrote:

Philosophy Explorer wrote:. Do you know what a function is?

Yes. A function is an event which is usually boring and at which inferior quality booze is dispensed in insufficient quantity.

How can you philosophize about something you know nothing about?

PhilX

Philosophy Explorer wrote: How can you philosophize about something you know nothing about?

What grounds do you have for supposing that I know nothing about the philosophy of mathematics? As it happens it's a subject I've studied in considerable depth over a period of some decades and thus the reason why I ask the question which you seem determined not to answer.

1. What is the philosophical significance of the point you're trying to make?

2. Should the above question be too difficult for you to answer then perhaps you could just divulge what in fact is the point you're trying to make?

Obvious Leo wrote:

Philosophy Explorer wrote: How can you philosophize about something you know nothing about?

What grounds do you have for supposing that I know nothing about the philosophy of mathematics? As it happens it's a subject I've studied in considerable depth over a period of some decades and thus the reason why I ask the question which you seem determined not to answer.

1. What is the philosophical significance of the point you're trying to make?

2. Should the above question be too difficult for you to answer then perhaps you could just divulge what in fact is the point you're trying to make?

The grounds? So far you've presented nothing to show otherwise, instead posting your nonsense. Same question.

PhilX