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0, odd or even?by repugno
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#1
Apr1907, 02:58 PM

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Is 0 an odd or even number? The reason why I ask is this:
I need to write cosh(x) as the sum of an even and odd function. I could only come up with cosh(x) = cosh(x) + 0, where cosh(x) would be the even and 0odd. However, this doesn't make any sense since 0 is exactly divisible by 2 with no remainder, hence it is even. So which one is it? 


#2
Apr1907, 02:59 PM

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0 is an even number.
But that has nothing to do with writing cosh as a sum of odd and even *functions*. 


#3
Apr1907, 03:15 PM

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The definition of an "even" function is that f(x)= f(x). The definition of "odd" function is f(x)= f(x). If f(x)= 0 for all x then f(x)= 0= 0= f(x) but also f(x)= 0= f(x) so f(x)= 0, the constant function, is both even and odd.
However, as matt grime said, that has nothing to do with the fact that 0 = 2(0) is an even number. cosh(x) is already an even function. sinh(x) is an odd function. In fact, e^{x}= cosh(x)+ sinh(x). cosh(x) and sinh(x) are the even and odd "parts" of e^{x}. 


#4
Apr2007, 09:58 AM

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0, odd or even?
0 mod 2 = 0, it means that 0 is even



#5
Apr2007, 11:25 AM

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In general, given a function f, you can write it as the sum of an even function and an odd function as follows:
[itex]f_{even}(x) = (f(x) + f(x))/2[/itex] [itex]f_{odd}(x) = (f(x)  f(x))/2[/itex] 


#7
Apr2107, 07:26 AM

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Okay, I'll bite: even?
Actually, a more interesting question would be whether 5 is odd or even. The number 5 is obviously odd. The constant function (which is what this thread is really about), f(x)= 5, is even. 


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