How to pronounce “integers” in English

integers, which are discretely ordered, right?

But what about the integers?

I have 30 integers.

algebraic equation over the integers, those are known as algebraic numbers.

The coordinates are integers or ??

the positive integers at once.

take the first billion integers and add them together, you're going to get a big number.

So they behave like integers in a quantization step.

purely in terms of integers.

Just like the integers 0, 1, 2, 3, minus 1, minus 2, minus 3, the number two happens after the number one

We have 1 bit integers, 8 bit, 16, 32 bit integers in the implementation.

Like that the sum of all positive integers up to infinity is negative 1 12th.

as a fraction of two integers.

And if you invert the integers to 17, it's like we were making a movie about current events.

The way that seemingly simple properties of integers, addition, and so on yields this wonderful rich complexity.

The sum of the first n integers is n times n plus 1 over 2.

And the nice thing about them being integers is that they are in the domain of all the mathematical functions.

Do you think that other sort of integers like format or display or the ways in which people interact with novels can be as form-bending as like pieces of a novel itself?

negative two, ranking the integers by their absolute value, their distance from zero.

but there are other ways we could well order the integers.

And the result that the some of the integers, we can debate about whether it's equal to minus 1/12 or whether it should be assigned a value minus 1/12.

infinite sums like our famous sum of the integers, which kind of brings us back full circle, right?

So show directly that if you add up the first n integers and square it, you get the sum of the first n cubes.

All we see is kind of a many natural integers.

So we'll call the product of these two integers N. So now what I do is I give you N and your

Motors today I think it's trending into the negative integers so I think this is a dynamic that takes place in every

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

Ordering them this way is actually what allows us to map the integers to the natural numbers and see that both sets are the same size,

That's a linear combination of the variables with the distances usually rounded to integers as the weights.

Very often there are patterns that are true for the first 10 integers and then they just go haywire.

For example, if we're looking at whole positive integers, the smallest is one.

If we can go ahead and get the presentation up so you can throw those 30 integers behind me.

- What are the integers and the real numbers- - Correct - and what is the line that Cantor was able to find?

So the next problem that one would consider where this method doesn't work is adding up squares rather than just consecutive integers.

Those little terms in parentheses in there are all sums of consecutive integers.

If S1 is the sum of the first n integers, then S2 is the sum of the first n squares.

And the key point is the monomial then can be added up to give us the powers of integers.

Because we want to get an x squared and that's the magic that lets us add up the first n integers.

The right argument gives the range of integers.

And of course, the plus reduce of the first n integers is really just the argument plus times 1

First pages is let's remind ourselves what integers are.

Now the Pythagoreans believed in the power of a very particular type of mathematics, based on integers.

it's just exactly the same as Hilbert's train again, because every fraction consists of two integers: the numerator and the denominator.

The integers and the rationals are all part of the

we said, are the numbers that come from the number line, including all the integers and the rationals and the algebraic numbers and

And I know in your book, you talk about the evolution, like how do we start with whole numbers and then integers

He's also a star on the Numberphile YouTube network, where his most popular videos include a discussion of Ramanujan's sum of all the positive integers--

There's an awful lot, I think, that people sort of say and assume about this, this sum of the positive integers.

So as a non-mathematician, I have to ask you, is it weird that you ask these questions about series of things that have integers in them.