My Math Forum Each even number is equal to zero
 User Name Remember Me? Password

 New Users Post up here and introduce yourself!

 May 8th, 2018, 12:37 AM #1 Newbie   Joined: May 2018 From: India Posts: 1 Thanks: 0 Each even number is equal to zero Dear Friends I have come to know an interesting fact that every even number is equal to zero and every odd number is equal to 1; what's your view? Last edited by skipjack; May 8th, 2018 at 05:06 AM.
May 8th, 2018, 01:34 AM   #2
Math Team

Joined: May 2013
From: The Astral plane

Posts: 2,162
Thanks: 879

Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
 Originally Posted by asitsikary Dear Friends I have come to know an interesting fact that every even number is equal to zero and every odd number is equal to 1; what's your view?
Okay, I'll bite. This is true if we are working in $\displaystyle \mathbb{Z} _2$ (or anything isomorphic to it.) But something tells me you are talking about something different.

Please tell us why you are saying that.

-Dan

Last edited by skipjack; May 8th, 2018 at 05:06 AM.

 May 8th, 2018, 03:22 AM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,660 Thanks: 2635 Math Focus: Mainly analysis and algebra I think that it's completely uninteresting until you explain yourself properly.
 May 8th, 2018, 04:27 AM #4 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,419 Thanks: 1025 Hmmm.....I wonder if any "integration" is involved....
 May 8th, 2018, 05:18 AM #5 Senior Member     Joined: Feb 2010 Posts: 706 Thanks: 140 I wonder how old he is? Zero or one?
 May 8th, 2018, 05:19 AM #6 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,660 Thanks: 2635 Math Focus: Mainly analysis and algebra Goodness knows. But if $2a=2a+2$, then $a=a+1$ if dividing by $2$ makes any sense. So $0=1$. Thanks from topsquark
May 8th, 2018, 07:29 PM   #7
Senior Member

Joined: Sep 2016
From: USA

Posts: 609
Thanks: 378

Math Focus: Dynamical systems, analytic function theory, numerics
Quote:
 Originally Posted by v8archie Goodness knows. But if $2a=2a+2$, then $a=a+1$ if dividing by $2$ makes any sense. So $0=1$.
To elaborate on this, what it essentially proves is that any field satisfying the OP's claims must have characteristic 2. This is another way of saying that division by 2 must not make any sense since it leads to a contradiction as you point out.

While I know you are aware of the distinction, I want to point out that the usual computation doesn't assume anything about invertibility.
The argument goes like:

If $2a = 2a + 2$, then $2a = 2(a+1)$. Since it holds for any $a$, it must hold in the case that $a$ is a unit and it follows immediately from uniqueness of inverses that $2a = 0 = 2(a+1)$. In a field, every element is invertible, hence the field has characteristic 2. The argument does not require any mention of inverting 2.

In fact, everything in this argument goes through equally well for arbitrary local rings. In this case, the characteristic is replaced by the Jacobson radical, but otherwise, there is no reason to mention inverting elements or requiring more than just the ring structure.

 May 8th, 2018, 07:48 PM #8 Math Team     Joined: May 2013 From: The Astral plane Posts: 2,162 Thanks: 879 Math Focus: Wibbly wobbly timey-wimey stuff. Good comments, but I just wonder when we'll hear from asitsikary. Unless, of course, he's a troll. -Dan
May 8th, 2018, 10:25 PM   #9
Senior Member

Joined: Nov 2010
From: Indonesia

Posts: 2,001
Thanks: 132

Math Focus: Trigonometry
Quote:
 Originally Posted by topsquark Unless, of course, he's a troll.
Or a spammer (There's a writing that something was edited by skipjack, probably a link).

 Tags equal, even number, number, odd number

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Shen Elementary Math 2 June 5th, 2014 07:50 AM Awesomo Abstract Algebra 2 May 29th, 2014 12:52 PM BenFRayfield Physics 0 August 25th, 2013 06:20 AM onur851 Number Theory 11 July 19th, 2013 02:25 PM onur851 Complex Analysis 5 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top

Copyright © 2019 My Math Forum. All rights reserved.