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Is infinity an odd number?

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andrew_t1000

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I write a LOT of assembler code, on various micro's.
At the moment I'm rewriting my 6502 fixed point math library for the Atmel micro-controllers.
Whilst wrapping (warping) my mind around 2's compliment math and having just watched the BBC documentary "Dangerous Knowledge", which is about the work of Georg Cantor, I started thinking about infinity.

Any number can be represented in any base, it's still the same number.
For example 13 in base 10, is 0d in hexadecimal, 15 in octal and 1101 in binary.

My premise goes like this,
Infinity expressed in base 2 would be an infinite number of bits, all 1's.
An infinite series that goes

2^0 + 2^1 + 2^2 + 2^3 ......... + 2^∞

If we only look at the least significant bit or digit, 2^0, which equals 1, then infinity should be an odd number.

Does this sound reasonable?
Am I missing something or have I been looking at these screens and 7 segment displays too long?
 
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Yuri_Armstrong

Guest
Infinity can't be an odd number because it's not even a number in the first place. Or at least that's what they taugh us in math class.
 
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Gravity_Ray

Guest
I agree with Yuri. Infinity is not a number.

But here is a couple of questions of my own.

Is zero positive or negative?

Is an electron male or female?
 
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adrenalynn

Guest
I'd have to concur - infinity is a concept, not a number, per-se.

Just don't go dividing by zero on that little Atmel. Errr - actually - try it! Might open a tiny little wormhole... ;)

(And you need to toss a message like the Vic20: "DIVISION BY ZERO IS A MATHEMATICAL ODDITY AND NOT ALLOWED") [As an aside that no one cares about except me: That was my first exposure to the concept of division by zero]

The fascinating part is how much more power that Atmel has than the original 6502. I love embedded processing. Reminds me of the halcyon days of yore.
 
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darkmatter4brains

Guest
That was a pretty neat thought though ;)

Infinity is weird, as is demonstrated by countable and uncountable infinite sets!

You can have one set, like the natural numbers (0,1,2,..) that is a countable infinite set, and another like the real numbers that is an incountable infinite set. Presumably, the real numbers have more elements in that set as there is not enough natural numbers to make a one-to-one correspondence between the two sets .... yet, they're still both sets with an infinite number of elements ... weird.

Projective geometry has really neat insights into infinity, and more weird stuff to go along with it
 
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andrew_t1000

Guest
I guess we shouldn't ponder this question too much, after what happened to Georg Cantor!
An infinite number of infinities?
That would drive anyone nuts trying to sort out.
That damn abyss is looking at me again!
If it doesn't stop it, I'm gunna thump it! :)

Zero is THE only number that has no sign and it is a number, not a concept, otherwise you would be able to divide by it.
As for infinity being a concept, is that definitive?

Don't we have any "real" scientists here?

For the record I was thinking about an integer infinity, not a real number infinity or a complex number infinity.


I still have a large stock of 6502's and support chips. As well as 6800's, 6809's, 8080's, Z80's and 68000's.
Modern micro-controllers do have an amazing amount of "grunt" these days, but for some projects I find a really fast clock speed a pain in the ass.
PIC's and Atmel's are great most of the time, but sometimes you need a micro processor.
Just like I still have a few DOS systems around for when I don't want a whole bunch of operating system in the way.
(That's DR-DOS by the way, not M$-DOS)
 
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adrenalynn

Guest
DOSBox gets the job done.

Define "real scientist"? I work as an applied mathematician, and put food on the table publishing and selling papers and patents. My post-grad work was in math and theoretical physics, and then a six year stint for our Uncle in math and applied physics. Then another twenty-plus years in theoretical and applied mathematics and computer science/EE. I know there are others around these parts with similar kinds of backgrounds...
 
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dryson

Guest
I don't think that infinity can be labeled a number being even odd or even. Infinity can however be measured with Pi. As long as Pi remains a partial function of the measure of mathematics and continues to have a remainder then until said remainder has been replaced by another remainder then the measure of the Universe could be said to be the remainder that is constant until replaced.
 
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ZenGalacticore

Guest
How can 'infinity' be a number?

Any number that claims it's 'infinity', can always use a zero.
 
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darkmatter4brains

Guest
I'll throw up another example, along the same lines, of why infinity is weird. Plus, it's pretty neat topic.

Take the set of natural numbers:

0,1,2,3,4,5,6, ......... (going out to infinity)

And take the set integers:

(going out to minus infinity) ......... -6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6, ......... (going out to infinity)

Now, which set has more elements in it?

Intuitively, you would want to say integers, but that would be wrong. It can be shown that a one-to-one correspondence can be set up between the two sets. That means for every element in the integers there is a unique element in the set of natural numbers. They have the same "number" of infinite elements - or in mathematical speak, they have the same cardinality. This cardinal "number" gets a special name, which if I remember correctly is called "chi" (insert greek letter here)

Some sets have a larger cardinality than the natural numbers, like the real numbers that I mentioned above, and they get a different symbol. Any set with the same cardinality as natural numbers is considered countably infinite, for obvious reasons. Any set with a larger cardinality than the natural numbers is considered uncountable.

Here's an excerpt from WIKI, which is okay, for more info:

A set is a collection of elements, and may be described in many ways. One way is simply to list all of its elements; for example, the set consisting of the integers 3, 4, and 5 may be denoted {3,4,5}. This is only effective for small sets, however; for larger sets, this would be time-consuming and error-prone. Instead of listing every single element, sometimes an ellipsis ('…') is used, if the writer believes that the reader can easily guess what is missing; for example, presumably denotes the set of integers from 1 to 100. Even in this case, however, it is still possible to list all the elements, because the set is finite; it has a specific number of elements.

Some sets are infinite; these sets have more than n elements for any integer n. For example, the set of natural numbers, denotable by , has infinitely many elements, and we can't use any normal number to give its size. Nonetheless, it turns out that infinite sets do have a well-defined notion of size (or more properly, of cardinality, which is the technical term for the number of elements in a set), and not all infinite sets have the same cardinality.

To understand what this means, we must first examine what it does not mean. For example, there are infinitely many odd integers, infinitely many even integers, and (hence) infinitely many integers overall. However, it turns out that the number of odd integers, which is the same as the number of even integers, is also the same as the number of integers overall. This is because we arrange things such that for every integer, there is a distinct odd integer: … −2 → −3, −1 → −1, 0 → 1, 1 → 3, 2 → 5, …; or, more generally, n → 2n + 1. What we have done here is arranged the integers and the odd integers into a one-to-one correspondence (or bijection), which is a function that maps between two sets such that each element of each set corresponds to a single element in the other set.

However, not all infinite sets have the same cardinality. For example, Georg Cantor (who introduced this branch of mathematics) demonstrated that the real numbers cannot be put into one-to-one correspondence with the natural numbers (non-negative integers), and therefore that the set of real numbers has a greater cardinality than the set of natural numbers.

In mathematics, an uncountable set is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related to its cardinal number: a set is uncountable if its cardinal number is larger than that of the set of all natural numbers.
 
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captdude

Guest
If an immortal being began writing down a number that represented infinity - he would NEVER finish writing. Therefore how could one ever say what the final digit would be?
 
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SpeedFreek

Guest
:D Ok, I'll chip in my pennies worth too!

How can infinity be an odd number if you can always just add 1 to it?

;)
 
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captdude

Guest
It would seem to me that adding 1 to infinity would be equal to accelerating another 1 M.P.H. past the speed of light. :?
 
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PandaPenguini

Guest
I don't think it's possible to say if it's odd or not, what i can do however is say that
the total number of numbers is going to be odd.

goes on forever--- (-1)_0_1 --- goes on forever

You can't think of them as the value but more of a tally-mark.
6,3,2,89 there are 4 numbers there.

So tally up all the numbers to the right of 0 and tally all the numbers the the left
Even if Infinity is odd there still is the inverse of infinity. Both sides of 0 are going to equal, then there is the final number, 0
making the total number of numbers odd.
 
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captdude

Guest
adrenalynn wrote

No, it wouldn't. It would just equal infinity.

You know I disliked my analogy as soon as I hit the submit button. I agree with you, thats what I was trying to imply by its statement.
 
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