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May 8th, 2018, 01:37 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 06:06 AM. 
May 8th, 2018, 02:34 AM  #2  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,980 Thanks: 789 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Please tell us why you are saying that. Dan Last edited by skipjack; May 8th, 2018 at 06:06 AM.  
May 8th, 2018, 04:22 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,557 Thanks: 2558 Math Focus: Mainly analysis and algebra 
I think that it's completely uninteresting until you explain yourself properly.

May 8th, 2018, 05:27 AM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,791 Thanks: 970 
Hmmm.....I wonder if any "integration" is involved....

May 8th, 2018, 06:18 AM  #5 
Senior Member Joined: Feb 2010 Posts: 701 Thanks: 136 
I wonder how old he is? Zero or one?

May 8th, 2018, 06:19 AM  #6 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,557 Thanks: 2558 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 $0=1$. 
May 8th, 2018, 08:29 PM  #7  
Senior Member Joined: Sep 2016 From: USA Posts: 534 Thanks: 306 Math Focus: Dynamical systems, analytic function theory, numerics  Quote:
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, 08:48 PM  #8 
Math Team Joined: May 2013 From: The Astral plane Posts: 1,980 Thanks: 789 Math Focus: Wibbly wobbly timeywimey stuff. 
Good comments, but I just wonder when we'll hear from asitsikary. Unless, of course, he's a troll. Dan 
May 8th, 2018, 11:25 PM  #9 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry  

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equal, even number, number, odd number 
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