Mummy, Mummy, what’s Russell’s Paradox?

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Eodnhoj7
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Re: Mummy, Mummy, what’s Russell’s Paradox?

Post by Eodnhoj7 » Tue Dec 19, 2017 6:08 pm

Arising_uk wrote:
Tue Dec 19, 2017 2:59 pm
Eodnhoj7 wrote:Thats the thing, some people say zero is a number and others say it is not. One is a number, plus it provides a foundation. ...
I think you're on shaky ground if you are looking to provide a foundation for Mathematics as Russell and Whitehead tried with Logic and only partly succeeded, mainly with the numbers as it happened.

Zero is only not a number if you stick with the natural numbers but if you do that you can't have the negative numbers, et al, which I doubt you'd want?

Would zero be a number without the set? ...
What are numbers in our Mathematics, functions. What do you think they are?
That is the question I ask, because if it requires a set to be a number than the set itself must be a number conducive to one.
Not sure what you mean here but, as best I understand it, a set doesn't have to be a number as it can be the empty set { }.
Instead of writing a long argument here is a summary of where I believe the foundations of mathematics should begin. It is a presented argument nothing more, but it provides the foundations for arithmetic, geometry and allows for sets. I am still looking for feedback on it, but so far it seems feasible.

viewtopic.php?f=26&t=23228

Viveka
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Re: Mummy, Mummy, what’s Russell’s Paradox?

Post by Viveka » Thu Dec 21, 2017 1:21 am

The natural numbers without 0 being a countable infinity are just as viable as integers with negative numbers and 0, being the same 'size'. Therefore, Johndoe has a point.

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Eodnhoj7
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Re: Mummy, Mummy, what’s Russell’s Paradox?

Post by Eodnhoj7 » Thu Dec 21, 2017 1:41 am

Viveka wrote:
Thu Dec 21, 2017 1:21 am
The natural numbers without 0 being a countable infinity are just as viable as integers with negative numbers and 0, being the same 'size'. Therefore, Johndoe has a point.
If what I am observing is correct, and I what to emphasize "if" as a very important point, the M.D.R arithmetic I am arguing for would provide legitimate foundations for numbers without us having to get rid of sets, or any extension of number theory developed in the past several hundred years.

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Arising_uk
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Re: Mummy, Mummy, what’s Russell’s Paradox?

Post by Arising_uk » Thu Dec 21, 2017 2:02 am

Eodnhoj7 wrote:Instead of writing a long argument here is a summary of where I believe the foundations of mathematics should begin. It is a presented argument nothing more, but it provides the foundations for arithmetic, geometry and allows for sets. I am still looking for feedback on it, but so far it seems feasible.

viewtopic.php?f=26&t=23228
But you don't accept zero as a number so how do you get to all the non-natural numbers?

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Eodnhoj7
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Re: Mummy, Mummy, what’s Russell’s Paradox?

Post by Eodnhoj7 » Thu Dec 21, 2017 2:12 am

Arising_uk wrote:
Thu Dec 21, 2017 2:02 am
Eodnhoj7 wrote:Instead of writing a long argument here is a summary of where I believe the foundations of mathematics should begin. It is a presented argument nothing more, but it provides the foundations for arithmetic, geometry and allows for sets. I am still looking for feedback on it, but so far it seems feasible.

viewtopic.php?f=26&t=23228
But you don't accept zero as a number so how do you get to all the non-natural numbers?
Zero is an absence of reflection, such as +1 reflecting -1. All non-natural numbers, if I understand you correctly, are merely an absence or deficiency in reflection and exist if and only if 1 exists, however are not things in themselves. 1 always exists however, therefore non-natural numbers exists as approximation of 1. Subtraction, division and roots are deficiencies and negative in value, while addition, multiplication and exponentiation are positive in value. Non-natural numbers are strictly deficiencies in natural numbers as approximations.

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Arising_uk
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Re: Mummy, Mummy, what’s Russell’s Paradox?

Post by Arising_uk » Thu Dec 21, 2017 2:15 am

But '1' doesn't exist as a thing in itself?

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Eodnhoj7
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Re: Mummy, Mummy, what’s Russell’s Paradox?

Post by Eodnhoj7 » Fri Dec 22, 2017 4:01 am

Arising_uk wrote:
Thu Dec 21, 2017 2:15 am
But '1' doesn't exist as a thing in itself?

It extends through all number, so it does. 0 is merely an absence of 1, and in these respects is an approximation of 1 if and only if 1 exists. While 1 can exist without 0, 0 cannot exist without 1.

However 1 always exists, therefore 0 is always observable.

Even our arithmetic functions are based upon positive and negative 1. Positive 1 reflecting a positive 1 is no different from addition in one respect, while simultaneously being the foundation for multiplication as positive (addition) reflecting positive (addition) to form further positive (multiplication as the addition of addition).

We can observe the gradation of 1 as unity into 1 as unit through division as one seperates itself through itself into itself. All fractions, as gradations of a potential unity, are the observation of 1 as reflecting negation as a boundary limit. Subtraction, division and root are all forms of negation in which we observe 1 reflect an absence, or cease to reflect. In these respects all negative numbers (and those that subtract, divide, root) are merely the limits of 1's unity.

1 is a thing in itself as all numbers, as things in themselves, are merely extensions of 1. Considering 1 is never changing, all structural extensions of 1 never change, and exist as things in themselves considering they reflect through 1 as a thing in itself. All numbers as extensions of 1, share the same qualities of 1 as 1 composes them.

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