August Spies

Jim, please show me geometric proof of linear infinity.

Like Jim said, it is not necessary to prove that linear infitinty exists for it to be a mathamatically sound idea. There are plenty of examples of such thigns in math, square root of -1 for example. They still make mathamatcal since.

Ierrellus

August Spies:

How does the concept of infinity contribute to mathematics?

Ierrellus

August Spies

hmm, that depends on what you mean. Does it practically help us much to talk about stuff that doesn't exist? I dont' really think so and I often argued that to math teachers, to no avail . But clearly allowing math to talk about the 4th, 5th, infinite demininsions expands math theory as a whole.

I dunno, im no mathamatician.

joedad

It's this

. . . . . . . . . . . . .

evolving into this

0 0 0 0 0 0 0 0 0 0 0 0 0

joe

Ierrellus

August,

You give an honest response. I sympathize with you in questioning instructors about infinity. When we deal with a linear system (lines, time, etc.), the only practical thing we can do, since we do not know of beginnings or ends, is to assert an arbitrary point on the line and to measure in each or all directions away from that point.

But we must utilize a given, which infinity is not!

joedad:

I love it!!!! How did you like Bill's neat scenario of a world of thirteen lines?


Ierrellus

[ April 30, 2002: Message edited by: Ierrellus ]</p>

James Still

Maybe it's just me but I don't get the point. Is this a refutation of Zeno a la Aristotle? Is this a critique against actual infinities? Is there an ontological component to all of this or are we talking purely mathematics? Surely you don't mean that a potential infinity is impractical? Come on Ierrellus throw us a bone!

Bookman

If nothing else, the refutation of Zeno's paradox has allowed the Calculus to solve to closed form many basic equations that form an apparently accurate model of how physical objects in the universe move (and for that matter, many, many other problems involving steady or mathematically describable rates of change.

Good enough for ya?

Bookman.

P.S. Don't forget about the contributions of infinite monkeys to literature.

MadMordigan

- - - - - - - - - - - - -

1. Is this a line interrupted by spaces?

yes

2. Is this a space interrupted by lines?

yes

I may be just a moron, but I fail to see why this is profound.

Mageth

I interpret it as "T T T T T T T T T T T T T".

owleye

James....

Your response intrigues me a bit. You are free to confirm or reject this, of course, but it seems it was near enough to what some have called a stipulated object. Alternatively, objects can be "treated as" what one has in mind for some particular concept. This feature of stipulation is different than other notions we might have of "seeing as" which puts more of the emphasis on perception, than does stipulation.

The question I'd have is how far is it legitimate to regard it (by way of stipulation) as a certain object in the direction of having no resemblance at all to the object stipulated. If I draw a circle, is it legitimate to treat it as a straight line (segment)?

Can the example at the head of the topic be considered as (treated as) any object whatsoever? If the answer is yes, I suspect the object is no longer being considered for what it is, but instead as a symbol for that which it is being considered. If this is true then, its value will then be subjected to some language element, and instead of falling under the umbrella of a perception, it will be entirely linguistic, losing all its original perceived meaning.

owleye