Holly shite! there are numbers that cannot be counted.. — Banno

Same with the odd vs whole. Oh it's *different* with infinities of infinities? This is not established in that video

Strictly, when properly stated, that's undecidable. But as I say, you need a mathematician.

Same with the odd vs whole — Gregory

Well, no, since for every whole there is an odd, as has been shown.

That you misunderstand something does not make it wrong.

It's useful, not true. — Gregory

Not true, but useful?

Ok, that really doesn't make any sense. Calculus is a part of mathematics and totally accepted. Please don't start to argue that Calculus is not true.

I've presented at least 5 cogent arguments against infinity — Gregory

No, you haven't been at all convincing. I'm afraid that you don't simply get it.

You can't seem to recognise that the responses you are receiving actually answer your questions. It's odd. But it's not about maths, it's about you. — Banno

I think I have to agree here with @Banno. Don't want to be harsh here.

Please don't start to argue that Calculus is not true — ssu

It's very first principles are wrong. Like in history when guys started questioning Euclidean postulates? Just because you misunderstood my arguments do not make them wrong. Have a good day

You are not the first to mistake their misunderstandings for something profound. I suggest you read and try to understand Cantor's diagonal argument - you should be able to Google a version you find agreeable. See if you can read it sympathetically, rather the deciding that it is wrong from the outset; that way you can avoid confirmation bias. it's hard stuff, and if you manage to see how it works you may find you have done something quite satisfying.

It's very first principles are wrong. Like in history when guys started questioning Euclidean postulates? — Gregory

How are the very first principles of calculus wrong? What are you talking about?

Actually you give a perfect example of something not being wrong, but simply limited. It's not that Euclid was wrong, it simply was the case that not everything fell into his understanding of geometry. Root cause was that geometry on a plane and on a sphere are simply different. And you might have to think of geometry of a sphere. That's it. Yet the geometry on a plane is still correct. Hence the error is if one thinks that all geometry happens on a plane. Thus there is Euclidian geometry and non-euclidian geometry (spherical or hyperbolic etc).



Actually, what example would really be false was the Greek idea that "All numbers are rational". And the idea why people believed it was so was because... math is so beautiful. Well, there are irrational numbers. The Greeks found them, and they weren't happy about it. Yet that idea really was a genuine error.

And I think that the idea that "there is no infinity in mathematics" is simply wrong. Similar to the latter example "all numbers are rational". That you only stick to finite mathematics is another thing. Ok, do that. But then what you can do in mathematics is limited.

This hoary false paradox certainly says nothing about the actual nature of space or anything.

In this exercise you are imagining the state of the tortoise/hare at a time closer and closer to the time that the hare catches up. But never reaching that time.

You can use this method to approximate this meeting time. No one does, since obviously it can be exactly solved. But if you perform enough iterations of the hare catching up and the tortoise moving on, you will arrive at the effectively exact time and distance that they meet.

The hare never reaches the tortoise, because time, in the thought experiment, never reaches the moment that the hare does pass. As soon as you imagine time proceeding beyond this meeting time, you must imagine the hare passing, for your thought experiment to tension consistent.

there are numbers that cannot be counted... — Banno

Only if you are a Platonic realist. Metaphysically, that's an issue with set theory in general, Platonism is presupposed.

And when abstractions such as numbers, are assumed to have independent existence just like physical objects, with no principles to differentiate between the abstract and the physical, we have the problem 180 mentioned:

confusing the physical and abstract. — 180 Proof

This is why the law of identity was imposed, as a principle of differentiation between physical objects and abstract objects. A physical object has an identity unique to itself, an abstract object has no such identity. Therefore all those assumed numbers which cannot be counted, have no identity.

...just like there are numbers that are even and numbers that are prime.