Indeed, sometimes one's choices don't matter to what happens eventually. On occasion the path forks and one's in a dilemma which one to take, one then does, after pondering deeply upon the options, only to find out later that both paths reunite farther down. Such things do happen. Makes me wonder if free will means anything at all!
It is because, for the Greeks, a number is a count (arithmos). It tells us how many of whatever thing you are counting. There can be no counting without a unit of the count, some one thing that is counted, apples, oranges, or fruit. An infinite or unlimited amount is not a number, it does not tell us how many. — Fooloso4
Also interesting is the whole number sequence: 0, 1, 2,...
From 0 to 1: That's something from nothing! Creatio ex nihilo. — Agent Smith
You're joking, right? — Agent Smith
The notion of arithmos emerges from the experience of counting. When we count, we always have a multiplicity of things before us. When faced with a single thing, we do not countit. If we say that it is “one,” we are speaking about its unity or we are asserting that it exists. One is not many. Therefore, “one”is not an arithmos.The first arithmos is “two. — An’ a one, an’ a two …
So, x = nothing (no, not zero, nothing), and x = ∞. That means ∞+1=∞. Mathematics breaks down! — Agent Smith
That's exactly what it means, it's basic calculus. — Pantagruel
Well, I won't say you're wrong. There must've been a very good reason why the Greeks were so reluctant to incorporate infinity into their math. Even Archimedes & Eudoxus, two people who were among the first to employ the method of exhaustion simply stopped/limited their calculations at/to an arbitrarily large but finite number (Archimedes used, if memory serves, a 96-sided polygon to approximate a circle when calculating ππ). — Agent Smith
What, may I ask, are the specific issues you have with ∞∞? Is it the paradoxes (Cantor's mind probably couldn't parse them and ergo, his brain crashed) or something else? — Agent Smith
And this is an example of mysticism? Obsession with lemniscates will lead to no good. Please see your psychoanalyst — jgill
The lemniscate, if you'll recall, was the reason Cantor lost his marbles. — Agent Smith
Infinity simply inreases the accuracy of our calculations and I guess that's why it's such a big deal. — Agent Smith
Well it makes for a lovely myth (sort of like Nietzsche going mad from his denial of God). He moved on from the lemniscate to the Hebrew alphabet before going mad, btw — jas0n
That's the only infinity that makes sense to me; kinda feel like a time traveler (physically in the 21st century but mentally a mathematical troglodyte) — Agent Smith
arbitrarily close — jas0n
Hage you heard of The Teakettle principle — Agent Smith
Aye! — Agent Smith
Infinity is used to get as close as possible to a target (curves/females). — Agent Smith
A 96-sided polygon isn't a circle but is merely circle-like, that's all. — Agent Smith
As you probably know, the old timers of math tended to feel that way...that only 'potential' infinity was respectable. But beyond what is accepted formally (say you embrace the symbol game of an infinite tower of differing infinities), an ancient problem remains. What does it all mean? To what does it all refer? How does it hook up with the rest of life? — jas0n
circle-like — Metaphysician Undercover
What if your die had an infinite number of sides, do you think it would be circular? — Metaphysician Undercover
Looked it up, and it's a big part of math. 'We'll transform this into a quadratic equation, which we covered last week...' — jas0n
The metaphysics, the ontology, of infinity, may not be as important as how useful it is to us. Figuring out if there are actual infinities or if they're just potential infinities would be the icing on the cake, yes? — Agent Smith
You wouldn't be able to tell the difference between an ∞∞-sided polygon and an actual circle. — Agent Smith
Have you heard of The Teakettle principle — Agent Smith
Your eyes, for sure, will find it really difficult to tell them apart, even your sensitive finger tips will fail in this task. — Agent Smith
I believe it's this very issue that you raise that makes infinity so attractive/appealing to mathematicians; You wouldn't be able to tell the difference between an ∞∞-sided polygon and an actual circle. Invoking Leibniz's 2nd law of identity (the identity of indiscernibles), I'd say it's all good; for all intents and purposes, won't you agree? — Agent Smith
We can reject infinity for many reasons, but look at all the good it's doing! — Agent Smith
Even having been a prof of mathematics I learn something about the subject on this forum. Never came across this. — jgill
IMO, there would be no difference at all. The phrase 'infinite-sided polygon' is typically interpreted as a circle. (Nonstandard interpretations are possible, of course.) — jas0n
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.