How to pronounce“infinities”in English

Some infinities like the set of square numbers, integers or rational numbers can be paired perfectly with the natural numbers.

These infinities like the set of all real numbers, the complex numbers, they can't be matched one-to-one with the natural numbers.

Some infinities are bigger than others.

of infinities that there could be infinity to the infinity power you know when you have kids someday they'll tell you i love you infinity you have to come

Would they be different infinities?

infinitely many infinities adding up still to the very same infinity, which is a strong instance, a strong violation of Euclid's principle once again, right?

Physicists don't like infinities, computer scientists don't like infinities, mathematicians love infinities.

are even greater infinities.

different types of Infinities that I want people to be aware of come from 1 2 3 4 5 6 that's what

these factorial types of Infinities 10 factorial 100 factorial a th factorial or um different per

kept getting these infinities and so he wrote a paper with rosen that he submitted to our most important journal physical

singularities these infinities and so the editor at that time and the part of it

construct the infinities and that's an issue right you cannot build up an infinity from zero but in practice you never do this right when you perform

So Cantor called these countable infinities, but then there are bigger infinities, Cantor called them uncountable.

And so we have an infinity of infinities of the train passengers together with the current occupants of the hotel, and everybody on the train wants to check in to Hilbert's Hotel.

So three different types of infinities that I want people to be aware of come from one, two, three, four, five, six.

There are different types of infinities, and which one you have depends on, in math, the type of mathematical infinity you're considering,

out though that those two types of infinities are actually the same type of infinity one is just multiplied by a factor of two over the other you're not getting a bigger infinity by counting

And the source of the infinities in quantum field theory is that particles hit each other.

when you're trying to do those infinities the regions that give infinities to feynman as soon as you get to those regions then

and you get a consistent theory of gravity without the infinities.

too many parts to count and when there are no infinities if there were two infinities you would be running into contradictions which is in some

to settle disagreements i don't think that you need infinities as or at all and you never needed them you can always deal with very large

that there are certain things that mathematicians can do dealing with infinities and by extension our mind can do

and electrons and all that he found that he's getting infinities he cannot resolve okay the natural conclusion is that

had all kinds of mathematical issues and all kinds of Infinities that cropped up and it was finally figured out more or less how to get rid of those but there

However, there are several different types of infinities.

by twos instead of counting by ones however there are several different types of Infinities so three

I mean, not that I believe in infinities, but I think the size of the book is growing.

einstein was and he saw that the way they set up the problem the infinities were like i might get as

which means it's no longer valid in order to deal with infinities and mathematics you have to postulate the existence in uh initially you cannot

numbers are not that large they're not googles or something the big the infinities that we are dealing with in our universe are mathematically

he got infinity and it didn't make any sense now there are similar infinities in the other pieces that but he had managed to make

this string starts to oscillate and these oscillation structure of the strings resolves those infinities to finite

Of course, the contemporary attitude about this situation is that those two infinities are exactly the same, and that Galileo was right in those

So, can you speak to the uncountable infinities?

And, in fact, instead of producing infinities, it produces correct results.

It turns out, though, that those two types of infinities are actually the same type of infinity.

But then I also want you to think of these combinatoric or these factorial types of infinities: 10 factorial, 100 factorial, 1,000 factorial,

which don't belong there the we call them coordinates singularities as a name but it but if you get these infinities

a student because if you don't set it up right in general relativity you get these infinities

sense what uh google and turing discovered in response to hilbert's call so there are no infinities there are no

the thing that he specifically refers to is the way in which human minds deal with infinities

these puzzles that feynman was having in calculating his diagrams and it gets rid of those infinities so

Because infinity is associated with God, how could there be multiple infinities?

So, laying that all out on the table, can you explain the idea of infinity, that some infinities are

This theory gives nonsense, because when you do the mathematics, you get infinities.

Infinity the numbers of itself they go to Infinity very very rapidly the probabilities of getting any particular outcome they go infinitesimal very very rapidly there are different types of Infinities

Now, what was realized in the early '70s is that if you replace particles by strings, these infinities go away