There is a natural means to specify "oddness" because that fractions. Because that integer $x$, allow $ u_2(x)$ signify the variety of $2$"s that division $x$. For example, $ u_2(6)=1, u_2(4)=2, u_2(12)=2, u_2(1)=0, u_2(7)=0$. We have the right to leave $ u_2(0)$ undefined, or set it same to $infty$, as you like.

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We can prolong this to fractions via $$ u_2left(fracmn ight)= u_2(m)- u_2(n)$$

This satisfies the lovely relation $$ u_2(xy)= u_2(x)+ u_2(y)$$which holds also when $x,y$ room fractions.

With this device in hand, us can define a number $x$ together "odd" if $ u_2(x)=0$. The product of 2 odd numbers is odd, if the product of one odd number and a non-odd number is non-odd. Yet there is no natural an interpretation of "even" numbers. We might take $ u_2(x) eq 0$ (but then the product of two even numbers might be odd), or $ u_2(x)>0$ (but climate we require a third term because that $ u_2(x)here.


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vadim123vadim123
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No, odd-ness and also even-ness is defined only because that Integers.

For more info: Parity


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answer Sep 19 "14 in ~ 15:41
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taninamdartaninamdar
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No. Same (whether a number is also or odd) only uses to integers.


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Scott CaldwellScott Caldwell
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Parity walk not apply to non-integer numbers.

A non-integer number is neither also nor odd.

Parity applies to integers and likewise functions. So i wouldn"t say that parity only uses to integers.

See more: The Main Source Of Nutrition For Vertebrate Neurons Is, Module 2 Flashcards

For instance, if $f(x)=x^n$ and also $n$ is one integer, then the parity of $n$ is the parity of the function.


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