However, with the inclusion of the negative natural numbers, and, importantly, , Z (unlike the natural numbers) is also closed under subtraction.

The set formula_5 of natural numbers is a discrete set.

Because this is the important idea behind whole number place value, decimal place value and fractions.

The numbers b 1 emax and b 1 emax (here, 1 10 95 and 1 10 95) are the smallest (in magnitude) normal numbers non zero numbers between these smallest numbers are called subnormal numbers.

How many natural numbers, numbers like 1, 2, 3, 4, 5, the numbers that you learn when you are two years old not including zero, not including negative numbers, not including fractions and irrational numbers, and decimals and all the rest, just regular counting positive numbers.

Super primes Primes with a prime index in the sequence of prime numbers (the 2nd, 3rd, 5th, ... prime).

The natural numbers 0, 1, 2, 3, and so on begin with 0 and continue upwards, so that every number has a successor.

Welcome to the presentation on adding and subtracting negative numbers.

Fermat also conjectured that all numbers of the form 22 n 1 are prime (they are called Fermat numbers) and he verified this up to n 4 (or 216 1).

But even numbers are only part of the whole numbers, all the odd numbers are left over, so there's got to be more whole numbers than even numbers, right?

that is, the real numbers is a bigger infinity than the set of whole numbers.

So on the number line, I just write all the numbers in order, and I go high enough just so I can so that all the numbers I am using are, kind of, in it.

Add up these figures.

(numbers percentage)

The aggregate numbers are overwhelming.

The numbers would get smaller.

It's called the number line.

So let me do a number line.

We went to the right 4 spaces on the number line.

Not because it's crazy, or anything, but because the fractions are ratios of whole numbers, and so are called rationals meaning the rest are non rational, that is, irrational.

Or we're going to go the right on the number line, because the numbers are getting bigger.

So, can we make a one to one match between the whole numbers and the set of all the decimals, both the rationals and the irrationals?

They are a form of numeral used for counting.

It is a central result in analytic number theory.

And the question is, are we going to see that big sweep?

Number theory Farisi made a number of important contributions to number theory.

It's the mathematics of prime numbers.

Well then you start going to the negative numbers.

We would have to extend the number line.

That's the number line.

We will do it orange. Plus 46. So we draw a number line here.

I will circle the numbers that are prime.

So let me draw a number line.

Let's draw a number line.

Well, we're on the number line.

Of course, the number line keeps going.

Introduce some negative numbers.

Now, one way to visualize complex numbers and this is actually a very helpful way to visualize them when we start to think about roots of numbers especially the complex roots

It is a very simple scheme that can be used to detect single or any other odd number (i.e., three, five, etc.

If you think about it on the number line, addition is increasing along the number line by that amount.

like we did in this presentation.

But what still bothers us is our distress over the fact that even numbers seem to be only part of the whole numbers.

So all we do is we go up the number line, or we go to the right on the number line, 4 more.

Character used for indicating positive numbers

Order specifies how to rank the numbers