Ask A Scientist Mathematics Archive

name         Melanie C.
status       other
age          40s

Question -   Is there any other reason for single-digit placeholder
zero to be considered an even number other than its placement on a number
line?
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Zero is neither 'even' nor 'odd' because the symmetries of  'even' x
'even' = 'even';
'even' x 'odd' = 'even' ; and 'odd' x 'odd' = 'odd'. Substituting zero into
these placeholders gives the result that zero is both even and odd which is
"reductio ad absurdum" and hence undefined.

Vince Calder
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Melanie C.,
The definition of "even number" tells us that zero is an even number.  Any
integer multiple of an integer is an even number.  Zero equals two times
zero.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College
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