The Mathematical Proof Thread

[Kernel Sohcahtoa]

[Kernel Sohcahtoa]

[pocaracas]

[Kernel Sohcahtoa]

Kernel, I think you're ready for this link: https://artofproblemsolving.com/community

(or have I shown it to you, before?)

You have shown it to me before, and it was in relation to math proofs.  The site looks pretty cool: I've certainly got a lot more to learn and could  always improve.  Out  of curiosity, is the site  being recommended due to poor/incorrect mathematical reasoning/proof-writing in my previous post? Thanks.

P.S. In general, to all AF members, if I've made an error in a proof/mathematical work that I've posted here, then if it's okay with you, could you please let me know, so that I can post a corrected version? Thanks, and I appreciate everyone's participation in this thread.  Live long and prosper.

[pocaracas]

[Edwardo Piet]

Kernel's humility and diplomacy is breathtaking and astounding.

All I've got going for me is my ability to constantly speak my mind. Or perhaps rather: my inability to fail to constantly speak my mind

[Kernel Sohcahtoa]

[pocaracas]

In your post, you said that you have a physics background. Out of curiosity, are you more interested in applied mathematics or pure mathematics (or do you like both)? Thanks again for your response.

I'd say I like both, but I prefer the applied variety.
Give me 3 dimensions and I can still visualize the thing.... go higher and things become tricky.

[LastPoet]

When you analyse an algebraic division Ring, a set E with with 2 operations called '+' and '*' with the axioms of the algebraic goup (E.+) previously proven with commutivity a+b = b+a, the exitence of one element we called 0 where for all x in E: x+0 = x, with the set not being empty or singular;

Given the properties of the operation '*':

1: there exists a member we call u where for all set members a, a*u = a
2: for all members of E, a*b = b*a
3: for all a,b,c in E, a*(b+c) = a*b+a*c

With these in mind prove that a*0=0 and while you're at it prove that 0 is not equal this 'u' mentioned on the axioms.

[LastPoet]

Also, this 'u' is commonly used in arithmetic as the number 1. The neutral set member in multiplication.

Our numeric system with the common + - * / operations forms a division ring.

I prefer an analytical approach to math.