Odd and even numbers

[user789653241]

Ds(9, yr5) asked me if decimal numbers can be defined as even or odd. I said no, but haven't got a clue why.

Can anyone give us some explanations please?

What do you mean by decimal numbers?

Odd and even numbers have to be whole numbers (integers). Full explanation at:

www.mathsisfun.com/numbers/even-odd.html

Wow... excellent question I've never thought about it!! At a guess I'd say that odd and even numbers are defined by whether, as wholes, they can be even shared into two halves.

I know what odd and even are, but what are decimal numbers. We have a decimal system, but a decimal number?

Even numbers can be divided by 2 to get a whole number. So negative numbers can be odd or even. 0 isn't either. Decimals aren't either. Just whole positive numbers 1 or more, and whole negative numbers -1 or less.

Love51 - so you're understanding decimal numbers to be decimal points? Like 0.5? I suppose they're not odd or even because they're not full numbers are they?

Thank you. Still bit stuck, tbh. Ds says, say 3.2 can be devided by 2 so why it's not considered even number. So it has to be a whole number?
Grrr...I feel I am so thick, tbh.

Gwenhwyfar, not sure. I always say decimal numbers. Is that wrong?

I assumed decimal numbers to be numbers that you refer to with decimal points. Eg 1.27 or 8.836. So they are not allowed to 'play' in the game of odds or evens :(

3.2 can be divided by 2 but so can 3! You just add on an extra decimal place and any number can divide by 2! But 1.6 isn't a whole number.
I get what he means, the final digit is either odd or even, but the number being odd or even only applies to whole numbers.

Yes, I just take it as a fact, but my ds with bit of ASD traits and obsessive nature wants more explanation than take facts as face value.

That link isn't quite correct. 0 isn't even. It feels it as it falls between two odds but zero is an anomaly. I'm trying to remember the proof why, but failing!

Thank you every one, I will let him read this thread tomorrow.

Get him to explain why 3 or 7 aren't even, that might help him make the link.

An even number is defined as 2n for n =...-3,-2,-1 0, 1, 2, 3..(all integers)
An odd number is (2n-1) for n = ...-3, -2,-1,0,1,2.3...

So yes, 3.2 can be divided by 2 but the result of that isn't an integer. 3.2 is a rational number

Thank you, Love51, I will do that.

I’m fairly sure zero is even.

Oh and yes, 0 is even

Love51 0 isn't a number.* It's not odd or even. It means zero - the absence of anything, that's why it's not a number.*

0 is most certainly a number!

Count in twos up from -5 to 5
Now count up in twos from -4 to 4

0 is even by any definition I know of.

odd/even is just a definition though as opposed to some fundamental thing, you could define it such that 0 was something other than even, it would make things complicated, as all the "rules" would start needing addendums
e.g.
even+even=even
even+odd = odd
odd+odd = even
odd + 0 = odd
even + 0 = even

is wasteful as it would work the same if 0 is simply even.

Every odd number has an even number 1 more than it, except -1, and every even number has an odd number 1 less than it except 1, every odd number has an even number in between it, except -1/1. etc.

An integer is even, if the last digit is even, except 0.

Simpler to just define 0 as even, as then all the rules are simpler, and there's no advantage to defining it as anything else.

0 is definitely a number!

An even number is defined as a multiple of 2. Normally, and certainly when defining even numbers, when we talk about being a multiple or divisor of something we mean an integer multiple or divisor. So e.g. a is a multiple of b if there is an integer n with a = b * n.

While you can also technically define a concept of divisibility on a field like rational numbers (fractions) or real numbers, it's not very interesting - everything except 0 divides everything else. So if you tried to define "even rational numbers" you'd just get "all rational numbers", not a very interesting subset.

I'd say that numbers with decimal points can be odd or even, but there you go. It all depends on where you put the point.

EG there are 350 pence in £3.50 and 350 is an even number. All you have done to it is move the decimal point. But then on the other hand, there are 35 lots of 10p and 35 is an odd number

"Ds says, say 3.2 can be devided by 2" Tell him that 3and 5 and 7 and 9 etc can also be dived by 2 (1.5, 2.5, 3.5 etc) so his test of odd or even would mean there are no odd numbers. Even numbers can be divided by 2 but the answer will be a whole number not a fraction or a decimal.

Haha @ sir "wasteful", cat "not interesting".

DS definitely comes up with most peculiar questions and I get since I just take known facts as it is without questioning.
(But I do love the fact that he thinks differently from me, questions and thinks about things in more original ways.)

I am still confused how I can explain this to ds, but I will let him read this thread and see how it goes.
Mrz's definition may work, as well as Love51's.

Thank you all, for your help.