Philosophical Illusion?

Terry Woods

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Join Date
Apr 2002
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3,170
So... you must have heard the question posed by the little girl, on the radio, to her Daddy...
"Why is the concept of odd and even a philosophical illusion?"

It sounds a bit like the tree falling with no one to hear.

But, maybe not...

We all know the basic definition of odd and even.

"n = 2k"

"n" is an even number for any integer "k".

... -4, -2, 0, 2, 4,... are all even (yes, even zero is even!)

But then it occurred to me... there appears to be a bit of an identity crisis in that "k" could be even or odd and yet "n" will always be even.

Some numbers are "really" even while others are "no so even".

I think the terminology is "doubly-even" and "singly-even".

That is, if an even number is divided by 2 and the result is even then the first number is doubly-even. From that point on, all subsequent devides by 2 will produce even numbers.

However, if an even number is divided by 2 and the result is odd...

ooops... gotta go...

Any thoughts?
 
Terry Woods said:
... if an even number is divided by 2 and the result is even then the first number is doubly-even. From that point on, all subsequent devides by 2 will produce even numbers.

I wouldn't try that with 12...
 
Terry Woods said:
I think the terminology is "doubly-even" and "singly-even".

That is, if an even number is divided by 2 and the result is even then the first number is doubly-even. From that point on, all subsequent devides by 2 will produce even numbers.

Any thoughts?

Look at it in the binary world. I can continue to divide by two (bit shift, if you like) until I have a 1 in the lowest bit. So, it all comes down to POWERS of two.

Take the binary number 10000000000000000, how "even" is that? 110110000000000000000 is "just as even," to use your terminology. But, in the end one of the divisions (the sixteenth) gets an odd number.

AK
 
Terry Woods said:
"12"

.... duuuhhh.....
Or even (no pun intended) "4". I guess this makes four the lowest 'doubly even' number. Hmmm, there's something odd about that!
 
Moin AK,

<quote>
Take the binary number 10000000000000000, how "even" is that? 110110000000000000000 is "just as even," to use your terminology. But, in the end one of the divisions (the sixteenth) gets an odd number.
</quote>

Always? What if the binary number is 0? It is even and it can be devided by two any number of times and the result remains even :)

Friedrich
 
OK then - can we agree that half the integers are odd and half are even? Then each 'singly even' number is the result of multiplying an odd number by 2. If we multiply ALL the odd numbers by 2 that gives us just as many 'singly even' numbers as there are odd numbers. Therefore we've used up ALL the integers. Therefore there can't be any 'doubly even' or higher order 'even' numbers. Or can there be? Hmmm.
 
Since nobody responded to my 'no doubly even or higher' note, let's try this. For each odd number you can create a 'doubly even' number by multiplying by 4. Likewise a 'triply even' number by multiplying by 8. And so on up you get 'Xply Even' numbers by multiplying by 2 raised to the X. So there's a whole lot of unique even numbers for each odd number! There must be a whole lot more even numbers than there are odd numbers. AHH - Terry, help me, my mind is going!
 
OK then - can we agree that half the integers are odd and half are even?
Well, no. It depends on how far you want to count.
-1 to +1 ........more odds
-2 to +2 ........more evens

The question becomes "is infinity odd or even?"
So there's a whole lot of unique even numbers for each odd number! There must be a whole lot more even numbers than there are odd numbers.
At best, only one more (or less), depending on your answer to above question.
beerchug
 
Gerry said:

The question becomes "is infinity odd or even?"

Finally someone mentioned the "I" word.

"Why is the concept of odd and even a philosophical illusion?"

That's why.

Philosophy should be confined to the pub. All questions of this nature can be resolved there.
 
Originally posted by Terry Woods

yes, even zero is even!

Terry

I might have to disagree with you on that one!

The defintion of 'even' (when applied to a number system) is an integer that is divisible by two with no remainder.

Zero cannot be divided by two. Does that make zero an odd number?

Well, if it isn't an even number then it must be an odd number, correct?

Probably not, as again, the definition of an even number is 'an integer that is divisible by two with no remainder'

With zero, there is no remainder, that makes zero neither odd nor even! So, what term are we going to use for 'zero'?..... Doubly-odd???

If there are doubly-even numbers then there must be a doubly-odd number, after all surely there is always an opposite, we need things to be balanced don't we?

We have ying and yang, land and sea, male and female, up and down, left and right, odd and even, so why can't we have doubly-even and doubly-odd?

My thoughts on this subject.

I agree with KennyB, this sort of discussions is best confined to the pub where you can talk a load of rubbish and still sound intelligent :rolleyes:

Paul
 

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