Register to reply

0, odd or even?

by repugno
Tags: None
Share this thread:
repugno
#1
Apr19-07, 02:58 PM
P: 79
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?
Phys.Org News Partner Mathematics news on Phys.org
Heat distributions help researchers to understand curved space
Professor quantifies how 'one thing leads to another'
Team announces construction of a formal computer-verified proof of the Kepler conjecture
matt grime
#2
Apr19-07, 02:59 PM
Sci Advisor
HW Helper
P: 9,396
0 is an even number.


But that has nothing to do with writing cosh as a sum of odd and even *functions*.
HallsofIvy
#3
Apr19-07, 03:15 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,534
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,
ex= cosh(x)+ sinh(x). cosh(x) and sinh(x) are the even and odd "parts" of ex.

alastor
#4
Apr20-07, 09:58 AM
P: 4
Wink 0, odd or even?

0 mod 2 = 0, it means that 0 is even
Jimmy Snyder
#5
Apr20-07, 11:25 AM
P: 2,179
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]
mathwonk
#6
Apr20-07, 10:28 PM
Sci Advisor
HW Helper
mathwonk's Avatar
P: 9,481
what about 6? is it odd or even?
HallsofIvy
#7
Apr21-07, 07:26 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,534
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.
mathwonk
#8
Apr22-07, 10:03 PM
Sci Advisor
HW Helper
mathwonk's Avatar
P: 9,481
good point, so the answer to the OPs question is "yes".

i.e. all constant functions are even and one of them is also odd.


Register to reply