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Is it reasonable to state the following?

Amouse Wed 13 May 05:44:39 2020 No.11666476 View Reply Original Report

Quoted By: >>11666479 >>11666487 >>11666631 >>11666650 >>11666752

If x*0=0, then x must be in the set of all complex numbers?

Anonymous

Anonymous Wed 13 May 2020 05:45:45 No.11666479 Report

Quoted By: >>11666480

>>11666476
Maybe, but less than 1 isn't the same as 1.

Amouse

Amouse Wed 13 May 2020 05:46:11 No.11666480 Report

Quoted By: >>11666482

>>11666479
I know?

Amouse

Amouse Wed 13 May 2020 05:47:32 No.11666482 Report

Quoted By:

>>11666480
Oh its you. Where did i say in my proof that less then one is equal to one?

Anonymous

Anonymous Wed 13 May 2020 05:50:33 No.11666487 Report

Quoted By: >>11666491 >>11666650

>>11666476
>If x*0=0, then x must be in the set of all complex numbers?
yes.

Amouse

Amouse Wed 13 May 2020 05:51:20 No.11666491 Report

Quoted By: >>11666498

>>11666487
Infinity is not contained within that set correct?

Anonymous

Anonymous Wed 13 May 2020 05:54:16 No.11666498 Report

Quoted By: >>11666504

>>11666491
only if you want it to be.

Amouse

Amouse Wed 13 May 2020 05:55:58 No.11666504 Report

Quoted By: >>11666549

>>11666498
Fuck you i dont

Anonymous

Anonymous Wed 13 May 2020 06:19:12 No.11666549 Report

Quoted By:

>>11666504
Wrong answer, fucko

Anonymous

Anonymous Wed 13 May 2020 06:58:30 No.11666631 Report

Quoted By: >>11666664

>>11666476
why forget about quaternions and octonions?
$\displaystyle \boxed{ \mathbb{T} \; \boxed{ \mathbb{S} \; \boxed{ \mathbb{O} \; \boxed{ \mathbb{H} \; \boxed{ \mathbb{C} \; \boxed{ \mathbb{R} \; \boxed{ \mathbb{Q} \; \boxed{ \mathbb{Z} \; \boxed{ \mathbb{N}}}}}}}}}} $

Anonymous

Anonymous Wed 13 May 2020 07:08:31 No.11666650 Report

Quoted By: >>11666664

>>11666476
No. It is true for $x = \omega$ but $\omega \not\in \mathbb{C}$.
>>11666487
Wrong.

bump

bump Wed 13 May 2020 07:13:00 No.11666664 Report

Quoted By: >>11666741 >>11666753

>>11666650
You forgot the funny math tags
>>11666631
I recognize none of the thingies outside of the complex numbers, can you tell me what they are?

Anonymous

Anonymous Wed 13 May 2020 07:49:17 No.11666741 Report

Quoted By:

>>11666664
for you to make a meaningful statement like "there exists a number x so that x*0=0", you need to first specify what system you are working in.

most useful systems that mathematicians have will require that for all x, 'x*0=0' but this is not always the case.

you need to think of things like the complex numbers, real numbers, integers, etc, less as canonical entities that exist, and more like puzzle sets that you take out and look at specifically. maybe your real number puzzle set will fit nicely inside your complex numbers puzzle set, but you may go to the store and buy a puzzle set that doesn't play nice with anything else.

Anonymous

Anonymous Wed 13 May 2020 07:54:25 No.11666752 Report

Quoted By:

>>11666476
x could be a matrix, a vector, a p-adic number, a member of a finite field, a polynomial ring and so many other things. None of those are in the set of all complex numbers.

Anonymous

Anonymous Wed 13 May 2020 07:54:41 No.11666753 Report

Quoted By:

>>11666664
You make the complex numbers by adjoining the number i (and all real multiples of i) to the real numbers. You can further extend them to the quaternions by adjoining the numbers j and k, which also satisfy j^2 = k^2 = -1, but also ij = k, jk = i, and ki = j, and furthermore ji = -k, kj = -i, and ik = -j. (Why these definitions are good ones is another story.)

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