Odd numbers are truly even?

Question

ok this is more of an abstract thought but since it's about numbers it belongs in the mathematics section. odd numbers are symettrical in that they have a naturally equal center point (lets call it piggy in the middle theory) whereas even numbers have to split a central number in two to be even. it's just one of those things that has always bugged me anybody got any far out thoughts on it?

Answer 1

Even just means that when you divide it into two equal parts, you'll have a whole number of items in each part. If you have 10 apples and you want to divide it in 2, you'll just have 5 apples and you don't need to slit any apples. If you have 11 apples, you're going to have to cut one of the apples in half. An even number of apples means that you don't have to cut any apples in half.

Even and Odd numbers really only make sense in discrete mathematics (apples) where you're dealing with whole numbers of objects. With continuous mathematics (liquids, sort of), the whole even odd thing doesn't really mean anything.

Answer 2

It kinda depends on how you look at it.

Even numbers are even because they can be halved equally to produce a whole number, i.e. 4 apples shared between 2 people, each person receives two apples, whereas odd numbers can't do this, i.e. 5 apples shared between two people, each person receives two and a half apples.

However, as you've stated it odd numbers are even as they have a whole number 'middle point', i.e.
1 2 3 4 5
......^ number three is in the middle, halfway through,
whereas even numbers the half way point is a decimal number, i.e.
1 2 . 3 4
.....^ the middle point would be 2.5.

This method doesn't include the number (or lack of number ;) ) zero. If you add this simple digit, the numberline theory corresponds nicely with the apples theory, i.e.
0 1 2 3 4
......^ two is in the middle
0 1 2 . 3 4 5
........^ 2.5 is in the middle...

It works with roman numerals as well

3 = III, half of three would be 3= Ii+Ii (use of the lowercase to indicate half)
4= IV or IIII, so half would be 4= II+II...

So really odd is still odd, even is still even and maths is still one of the most confusing things in existance!

Answer 3

You are seeing this:

odd number is 2n+1 where n = 0, 1, 2, 3, ....

Odd number can always look like:
n+1+n and so has a symmetry property.

Even numbers look like 2n where n = 0, 1, 2, 3, ....

so can be written as
n+n with "nothing" in the middle.

But the idea of "even" means you can split something with a friend and with "odd" you always have the "naturally equal center" left over!

Answer 4

I see your point. Its not mathematics but philosophy. The thing is to do with labels. Are labels the right ones or not. Try this for instance 50p is worth more than £50 in real terms because the metal used is more valuable in the long term. Take away the label and you will see things more clearly. like 2 + 3 = 2 ( when 1 box contains 2 and another contains 3 , you have an answer of 2 really!)

Answer 5

Odd numbers. I guess I'm a little odd too. 7 is my birthday. I like things displayed in 3s. I like company in 3's rather than two. I like to be by myself(1). I like 1 of anything on my plate. when I bet the lottery I pick more odd numbers. The list goes on....

Answer 6

As far as I am aware you only get an even number if you add two odd numbers together! [ref 1]
e.g. 1+1=2, 3+1= 4 etc.
or two even numbers together
e.g. 2+2 = 4 etc.

Anything can be symmetrical - it just depends where you define your axis of rotation, plane of reflection or translation. But it is a characteristic usually associate with geometrical shapes rather than numbers . . . [ref 2]

Hope this helps

Answer 7

even numbers do not have to split a number in two to be even, infact it is the other way round. If you are given 6 melons to split between you and your friend, you will both end up with 3 each. However, if you have 7 melons between you, you will end up with 3 and a half melons each.

But what happens when you can't split into equal halves, such as sharing out money???

I think you just have to accept that odd numbers are odd, and even numbers are even......

Answer 8

Pythagoreans could answer this problem.

Something to do with patterns/shapes that numbers make. Odd numbers make different patterns from even numbers. For instance, you can't make a square or rectangle from an odd number.

Answer 9

by defination odd numbers cannot be divded by two or into two equals without going into fractions.

centre point is a nice idea but it takes away a part of the number itself.

Answer 10

You are missing the number zero in your thought.

Think in binary terms and every thing is either one or zero. Odds have one in the middle. Evens have zero in the middle.

They are both symmetric. You are just missing the zero.