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.

You are watching: Can fractions be even or odd

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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edited Apr 13 "17 at 12:21

CommunityBot
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answer Sep 19 "14 in ~ 15:59

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

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answer Sep 19 "14 in ~ 15:41

taninamdartaninamdar
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No. Same (whether a number is also or odd) only uses to integers.

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reply Sep 19 "14 in ~ 15:41

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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edited Sep 19 "14 in ~ 16:12
reply Sep 19 "14 in ~ 15:55

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