Mathematical Infinity

After all, isn't number as number essentially specific?

One place infinity pops up is in irrational numbers, numbers such as pi and the square root of two which are given by an infinite decimal representation like 3.141596535... and so on forever without repeating.

I think infinity is actually a discrete number to be honest.

Well, that's an interesting statement. I think you should present your reasons, for on the surface it sounds paradoxical. After all, finite and discrete are synonyms in my book. Welcome, in any case, to the discussion. And please elaborate.

In this world, for example, infinity is a number - it is albeit a very huge number. We are limited by quanta, huh.

Even our minds could only think of a number that is very small compared to this number, but it is discrete - we just couldn't think of it due to our small brains.

I want to fire up a discussion of infinity in the mathematical sense. Is it a number? A concept? Is it thinkable? Is it usefully vague? Is infinity a sort of anti-number? After all, isn't number as number essentially specific? Is infinity some strange informal function?

Is thought essentially finite? Is the concept of infinity a finite concept that refers away from its own nature? I think we can easily include the infinitesimal in this discuss, as it seems to be the reciprocal of infinity, or 1/infinity.

Thoughts?

How does a number have no beginning nor an end? Even PI begins with a three. A number cannot go on for infinity as numbers always start somewhere. They might go on for a long time, as with PI, but a long time is not infinity.

I do not believe it would be possible to have this conversation if concepts of infinity were not thinkable.

Is infinity useful? Only when discussing the Infinite Supreme it neither applies nor exists anywhere else.

As far as an anti-number, infinity is to numbers as darkness is to light.

How does a number have no beginning nor an end? Even PI begins with a three. A number cannot go on for infinity as numbers always start somewhere. They might go on for a long time, as with PI, but a long time is not infinity.

Is infinity useful? Only when discussing the Infinite Supreme it neither applies nor exists anywhere else.

Take a triangle with two 72 degree angles, bisect one of these angles with a line meeting the opposite side of the triangle. You'll have drawn a similar triangle. This process can be continued infinitely, thus demonstrating the irrationality of the golden ratio.

We should acknowledge, I think, that infinity is indeed useful in math. For instance, 1/x. As x tends toward infinity, the expression tends toward zero. What I love about math, among other things, is that it reveals the structure of human thought. No magnitude is the final magnitude. And this is fascinating. Therefore the invention of mathematical infinity. Are you familiar with Cantor? Very fascinating stuff. I just read a good book on him. He used the aleph, which is the first letter of the Hebrew alphabet, to represent his transfinite numbers. This aleph is connect to the Kabbalah, and the Ein Soph, and also to Elohim. And yet this mysticism inspired mathematics is real mathematics, and from what I've read, Cantor's vision is set theory is the standard now. Cantor showed that there are as many numbers between 0 and 1 as there are between 1 to infinity, as strange as that may sound. And some other amazing things as well. His technique was to use a diagonal method and put numbers into one-to-one correspondence.

---------- Post added 04-10-2010 at 11:04 PM ----------



I agree. But my point would be that our concept of infinity is nothing more than the negation of our concept of the finite. -finite, you might say. Of course this negative of finity must be understood in terms of the number spectrum. It's a piece in the lingual-numerical-spatial game of mathematics.

---------- Post added 04-10-2010 at 11:08 PM ----------



Well, it is quite useful here and there. It's an abstraction that functions usefully as shorthand. Let's compare one to google (which is one followed by one hundred zeros) to one to infinity. Infinity is that strange concept that names the pseudo-end of an endless spectrum. THe concept is a bit paradoxical. And yet calculus, to my knowledge, was invented by using its reciprocal, the infinitesimal, and calculus seems to be perhaps the great leap in the history of mathematics, as the real world is in motion. I think it all goes back to Zeno's paradoxes.

Take a triangle with two 72 degree angles, bisect one of these angles with a line meeting the opposite side of the triangle. You'll have drawn a similar triangle. This process can be continued infinitely, thus demonstrating the irrationality of the golden ratio.

Nullity and infinity and negative infinity and the imaginary infinite all pickled my interest for some time. I noted that the negative and the imaginary were both adjectives unto infinity and so figured them likewise in some fashion. So it seems Mr. Buckminster Fuller was on the right path in regards to mathematics.

But there is a certain idolatry going on with the presentation of infinity as actually a number when our base ten system will never reach anything other than what it already contains-- and never reach any number we might call infinity.

Are we wishing to speak of different systems when we bring infinity to the table? It doesn't seem that infinity is the answer to any question.

If infinity is contained in the number, then no number could capture infinity.

I guess an analogy could be made: If God is contained in the word, then no word captures God.

What number is it?

Infinity has no beginning nor end.

Nullity and infinity and negative infinity and the imaginary infinite all pickled my interest for some time. I noted that the negative and the imaginary were both adjectives unto infinity and so figured them likewise in some fashion. So it seems Mr. Buckminster Fuller was on the right path in regards to mathematics.

But there is a certain idolatry going on with the presentation of infinity as actually a number when our base ten system will never reach anything other than what it already contains-- and never reach any number we might call infinity.

Are we wishing to speak of different systems when we bring infinity to the table? It doesn't seem that infinity is the answer to any question.

If infinity is contained in the number, then no number could capture infinity.

I guess an analogy could be made: If God is contained in the word, then no word captures God.

Bigger similar triangles can also be constructed, infinitely.