/sci/ - Science & Math » Thread #13032904

7KiB, 200x200, wojak-smirking-thumbnail[1].jpg

View Same Google iqdb SauceNAO

Anonymous Mon 26 Apr 08:19:07 2021 No.13032904 View Reply Original Report

Quoted By: >>13033255 >>13035258 >>13035358 >>13036625 >>13036709 >>13036716

>you can't prove that multiplication is commutative for all reals

Anonymous

Anonymous Mon 26 Apr 2021 08:38:13 No.13032959 Report

Quoted By:

Assume a * b is b * a.

Then b * a = a * b.

So our ekveyshun is a * b = a * b

The b's canclel so its a = a.

Move the other a to left

a - a = 0

Use distributeivtity: a(1-1)=0

1-1= 0 because if you have one

apple and you take one apple you have sero aples

Anything times zero is zero

so 0 = 0

Which is obivous Q.E.D.

Anonymous

Anonymous Mon 26 Apr 2021 10:42:27 No.13033255 Report

Quoted By:

>>13032904
Follows from the commutativity of the rationals .

Anonymous

Anonymous Mon 26 Apr 2021 19:44:40 No.13035258 Report

Quoted By:

>>13032904
isnt that an axiom

Anonymous

Anonymous Mon 26 Apr 2021 19:57:34 No.13035358 Report

Quoted By:

>>13032904
rationals commutative -> trivial proof of commutativity by unpacking your favorite construction of the reals. Dedekind cuts, equivalence classes of Cauchy sequences, the proof is more or less the same.

Anonymous

Anonymous Mon 26 Apr 2021 23:47:55 No.13036625 Report

Quoted By:

>>13032904
For all positive reals, a, b
log(ab) = log(a) + log(b)
Addition is commutative
= log(b) + log(a)
= log(ba)
log is single valued
hence ab = ba
Extending proof for negative reals is left as an exercise, because I'm drunk.

Anonymous

View Same Google iqdb SauceNAO tarski's axioms.jpg, 113KiB, 1170x721

Anonymous Tue 27 Apr 2021 00:13:10 No.13036709 Report

Quoted By:

>>13032904
*characterizes $\mathbb{R}$ without mentioning multiplication

Anonymous

Anonymous Tue 27 Apr 2021 00:15:07 No.13036716 Report

Quoted By:

>>13032904
real numbers are the limits of some cauchy sequence, {x}*{y} = {x*y} = {y*x} = {y}*{x}
fuck off

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches