Hello,

I have the following question:

If the definition that was incorrect, would that have any impact on the different mathematical disciplines.

Or to put in other words: what would the consequences be on mathematics (in general) if .

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- Dec 10th 2013, 04:20 PMsurjectivemath question
Hello,

I have the following question:

If the definition that was incorrect, would that have any impact on the different mathematical disciplines.

Or to put in other words: what would the consequences be on mathematics (in general) if . - Dec 10th 2013, 04:31 PMPlatoRe: math question
Look at this thread .

- Dec 10th 2013, 07:20 PMsurjectiveRe: math question
Thanks for the reply.

From the thread that you directed me to I understand how to derive at .

My question, I feel, is not sufficiently answered. I would like to know whether there are any areas of mathematics that "break down" if this equation does not hold?

An analogy would be: What difficulties would mathematics suffer if .

I had a discussion with a person and it got me thinking. - Dec 10th 2013, 07:22 PMProve ItRe: math question
Well for one thing, you would have a direct contradiction to the other index laws. There is nothing else that can possibly be besides 1, at least when .

- Dec 10th 2013, 09:33 PMsurjectiveRe: math question
Hello,

I think I see what you mean but could you, for the sake of clarity, give one or two specific examples?

Are there other areas where things would "go wrong" ? - Dec 10th 2013, 10:21 PMromsekRe: math question
the laws of exponents wouldn't work. You might as well ask what would happen if addition didn't work.

You would multiply things by 1 and not end up with what you started with. Everything would either blow up or implode depending on whether was greater or less than 1.

None of the laws of physics would work if the laws of exponents didn't work. - Dec 10th 2013, 10:24 PMtopsquarkRe: math question
- Dec 11th 2013, 03:30 AMsurjectiveRe: math question
I see. Could anyone show me an example of the exponent laws not working if you made the assumption that ?

This will be my last request. Thank you very much. - Dec 11th 2013, 04:23 AMtopsquarkRe: math question
- Dec 11th 2013, 04:33 AMsurjectiveRe: math question
Thanks everyboby :)

- Dec 14th 2013, 04:09 PMPlatoRe: math question
Actually for a whole school of modern analyst

**it is true that**.

We think that is defined if and only if .

We believe that it far better to go with the ideas from modern*non-standard analysis*of a enlargement.

Add one new*number*, , to the real number system.

We define the number as being a root of the equation

There is a group centered is St Louis calling for a more geometric approach to complex numbers.

But I say that using the enlargement idea is just as natural.

Look at this. If then and it is a root of !

Hence it seems as if .