My theory that all numbers are odd numbers.?

Question

Actually, its just a paradox, but it goes like this.

There is an infinite amount of numbers. Which means there is an infinite amount of odd numbers. The amount of odd numbers in existance is EXACTLY equal to the amount of numbers in existance, because infinite = infinite exactly. If the amount of odd numbers is EXACTLY equal to the amount of numbers, then all numbers must be odd.

Same can be said about Even numbers.

So, actual question: Is this paradox idea original? And, Do you like it? Does it make any sense?

Existance = Existence, whatever.

Its not actually a theory, its just a paradox, and I think 'infinite' indeed reprersents a numerical amount just like any number.

Mr.Florida:

You pointed out an algerbraic flaw in infinite. and because of that, it does not constitute as a valid mathamatical number. Is that right?

So I got something you'll like, perhaps you've already heard of it.

1=1

1/3 = p
1/3 = 0.333...
0.333.... = p

3p = 3p
3(1/3) = 1
3(0.333...) = .999...

1 = .999...

Algebraicly, 1=.999..., Does that make any sense? Clearly a flaw. Instead of saying '1=1', I guess we have to say 'the concept of 1 = the concept of 1'.

Answer 1

The flaw in your logic is that you assume that one infinite quantity is identical to another. But really the only thing you can practically say about anything infinite is just that there is not a finite number of elements.

If you want to compare one infinite set to another, there are ways of doing this. One common way is to match elements together.

So, for example, we could match whole numbers and odd numbers. It turns out that every odd number is also in the set of whole numbers, making matching really easy. But in addition, the set of whole numbers has an even number for every odd number. Thus we can confidently say not only that the set of whole numbers is larger than the set of odd numbers, but that it is exactly TWICE as big. Even though they're BOTH infinite.

And so it goes with other sets. The set of all odd numbers is one element larger than the set of 'all odd numbers except for the number 3'. And they're still both infinite.

It's a common misunderstanding of the infinite really. I've seen it a number of times. Hope that helps.

Answer 2

I'm going to have to Vote "No" here - on all points. No it doesn't make sense and no it's not that original. Sorry, that came out so snarky! Using your theory we could say that all numbers are prime numbers, or that all numbers are really not even numbers at all but something else entirely. It's just too open ended. Mathematics - for all its chaotic beauty - does have rules and deciding which numbers are primes, even, odds, etc. is part of the framework that makes all the fuzzy logic stuff possible. Regardless, judging from this question you sound like someone who digs numbers and can probably wrap your head around some freakydeaky stuff - you should check out "Just Six Numbers" by Martin J. Rees, I'm reading it now even though it's a bit over my head. It's well written and really gets the brain going. Give it a try.

Answer 3

Infinity is not a definitive number, but a concept. Saying infinity is equal to infinite, can be better stated as "The concept of infinity is equal to the concept of infinity".

I guess you would have to theorize my following equation to determine if what you're saying is correct.

Is this formula true: x+(infinity)=infinity....

consider that if you treat infinity as a 'definitive number', you can simplify the equation by saying x=(infinity) - (infinity)...
which means that x=0.

But as you plug in numbers to X, you find that the final result is incorrect. Which shows that 'Infinity is only a concept, and can not be applied to the logistics of mathematics in a numerical sense.

Edit: 1/3 doesn't equal .333...-- .333 with an infinite amount of 3's---and considering the above info with the concept of infinity not being a definitive number, .333 with an infinite amount of 3's is not a definitive number either. I don't have to prove it numerically because you did it for me. The issue is not the 'concept of 1's', but error is in the 'concept of infinity'.

Answer 4

You can't divide an odd number by 2 without getting decimals or fractions. That is not the same sorry.

- About the second one 1 doesn't equal to .99... because we put an approximate sign there. So it's still not equal.

Answer 5

I see what you are saying, it in a way it makes sense...

BUT in reality, you're theory does not work for even numbers as well, because even numbers you can divide by 1 or more numbers, even or odd.

Odd numbers you cannot.

There are an infinite amount of odd numbers as well as even numbers, but they are not all odd or even. As we learned at a very young age: Odd numbers are odd, and even numbers are even.

Answer 6

It will never cease to amaze me...how many people write their "answers" to questions without ever addressing the issues actually raised by the questioner. As I'm sure you agree with me Nosey, no one has yet touched the intention of your question, so let me point out a few things to show you the way...

No it's not an original paradox, though I'm sure you did come upon it in your own thinking. This is actually one of the many questions that the concept of infinity raises in mathematics. It does make sense on some level, but not in the way in which you present it.

One issue that I must raise is that you use the terminology "numbers in existence", and this is not advisable. Numerals (not "numbers", 1, 2, 3, etc. are called numerals) are not existant objects, they are abstractions and concepts. Mathematics is a "formal system" meaning a syntax which consists of linguistic entities (numerals and their dancing partners) along with manipulation rules. Any resemblance mathematics has to the "real world" is an intentional coincidence (just to bring in another paradox *wink*).

So to say the number of even numerals "in existence" is equal to the number of odd numerals "in existence" is nonsense. No numerals exist. That in itself removes the literal paradox you have constructed, however there are still deeper paradoxes created by the concept of infinity and its relationship to math.

Mathematics is much more complicated than what most of us learn in school. They teach the manipulation rules but not the story behind them, not the reasoning or purpose of the problems we are told to solve. One must keep in mind that there are more than Positive Integers to deal with, there are real numbers, irrational numbers, natural numbers, negative numbers, and who knows how many other crazy things.

This answer is getting too long, but I would like to quickly bring up a couple more paradoxes that are better than yours, that you should enjoy, and a couple things for you to read up on.

What about the infinity of numbers between each positive integer? With repeating decimals (that some people are going to claim are equal to a whole number) and the "irrational numbers" which are nonrepeating infinite decimals created by application of the diagonal method (see Cantor below), there are an infinity of numbers between every natural number. How bout that one?

You should read about the German Mathwhizz Georg Cantor and his possible foundation of math called "Set Theory" it has all kinds of great paradoxical findings. And if you want to learn more about the mathematics of infinity check out the book "Infinity" by Brian Clegg, it's pretty cool.

Hope you finally got your question addressed!

Answer 7

Quite simply your logic is flawed...

Any sequential set of numbers always generates (approximately) 50% odd numbers and 50% even numbers. So, a set called infinity would generate 50% odd numbers. Thus, the series of odd numbers that goes to infinity is smaller than the series of all numbers that go to infinity.

Answer 8

The problem with your theory is you are treating infinity like a number when it is more like a formula.

Answer 9

hmmm, interesting. But infinite does not mean all. like a line, it goes on for infinity but it does not contain alll space (since it extends in only 2 directions in a linear fashion).

Answer 10

Well, infinite doesn't represent a numerical value. Sorry.