# Facebook math

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## Facebook math

https://brilliant.org/community-problem/a-problem-by-arul-kolla/?group=i2KL1625hqMK

(What is 2^2014 - 2^2013?)

I didn't want to comment on the facebook link, so I'll write crap here.

This is a series of characters and formatting, presumably to represent a mathematical expression using arabic numerals of base ten. To expand on that: This expression presumably uses elements of the ring integers (We'll call this set Z) under standard addition and multiplication (We'll call this ring ZR). The term - is presumably shorthand for the function -:ZR->ZR with a-b = a + b * -1 given a,b in ZR. The ^ operator (superscript in the link) is not a ring operator, but, assuming it is standard exponentiation, it is trivial to show ^ is closed for the left operand an integer, and the right operand a positive integer, and therefore should cause no problems with evaluation of the expression. I will also assume we are following the standard notation, which requires operations of ^ to occur before operations of - or + or *. In that case, it is fairly simple to evaluate the expression, assuming it is to be evaluated alone. 2^2014 - 2^2013 can be rewritten as 2*2^2013 - 2^2013 or (2-1)2^2013 using the distributive property of rings. We are also using the ( ) as a notation for precedence of evaluation, so (2-1)*2^2013 = 1*2^2013. We know 1 is the multiplicative identity of the ZR ring, therefore 2^2014 - 2^2013 = 2^2013.

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Math class withdrawal sucks

(What is 2^2014 - 2^2013?)

I didn't want to comment on the facebook link, so I'll write crap here.

This is a series of characters and formatting, presumably to represent a mathematical expression using arabic numerals of base ten. To expand on that: This expression presumably uses elements of the ring integers (We'll call this set Z) under standard addition and multiplication (We'll call this ring ZR). The term - is presumably shorthand for the function -:ZR->ZR with a-b = a + b * -1 given a,b in ZR. The ^ operator (superscript in the link) is not a ring operator, but, assuming it is standard exponentiation, it is trivial to show ^ is closed for the left operand an integer, and the right operand a positive integer, and therefore should cause no problems with evaluation of the expression. I will also assume we are following the standard notation, which requires operations of ^ to occur before operations of - or + or *. In that case, it is fairly simple to evaluate the expression, assuming it is to be evaluated alone. 2^2014 - 2^2013 can be rewritten as 2*2^2013 - 2^2013 or (2-1)2^2013 using the distributive property of rings. We are also using the ( ) as a notation for precedence of evaluation, so (2-1)*2^2013 = 1*2^2013. We know 1 is the multiplicative identity of the ZR ring, therefore 2^2014 - 2^2013 = 2^2013.

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Math class withdrawal sucks

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## Re: Facebook math

I tried to submit the answer on that website but it said I had to register in order to do so. As if I'm going to give them my personal information so I can do math problems. As if my college classes don't give me enough math problems to do...

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