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Is Zero even?

September 18, 2018

Jo Gledhill (@JoLocke1) asked this on Twitter:

… thoughts on 0 being even or neither!! Some of my dept say neither I say even as a multiple of 2 sorry?!?!?

Here’s my thoughts about what makes something even as it’s something that comes up in my classes often when I’m doing the caterpillars investigation.

Even numbers end in 0, 2, 4, 6 or 8

This one often comes up with students and I’d agree with the caveat that we’re talking about integers. I wouldn’t want to have to say that 1.2 is an even number for example.

Even numbers are (integer) multiples of two

Passes this test. 0 = 0 × 2

Stacking up a pile of blocks

If you stack up the blocks into two piles, the top is level (even). This works with 0.

Sharing it out

When you share an odd number of things equally between two people, you have an odd one left over at the end (remainder one). That doesn’t happen with two.

It fits the pattern

-3, -2, -1, 0, 1, 2, 3

odd, even, odd, even, odd, even, odd

So, in conclusion

0 is even


In other 0 related news:

0 is neither positive nor negative

0 may be a natural number or not, depending on which definition you use!




From → Maths

  1. Adam Atkinson permalink

    It’s both positive _and_ negative if you are French.

  2. Adam Atkinson permalink

    You would need to ask some French mathematicians but if I understand correctly to say what most of us would call “positive” they would say (the French for) “non-negative” or “strictly positive”. Where else does this happen? Well, I have no idea.

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