The positive integers are the numbers we count with.

So, we shall see in that lecture how to count.

How do we count? We first count on our fingers.

On one hand, we have the five first digits 1, 2, 3, 4, 5.

The 10 fingers of both hands are the digits 1, 2, 3, 4, 5, 6, 7, 8, 9.

Oh no, there is not 10.

This is because 10 is not a digit.

It is a group of 10 objects written 1, 0, 0 is for no object.

And 1 is for one group of 10 objects.

This is the 10 basis numeration.

We use the 10 basis numeration because we have 10 fingers.

Let's continue with marbles.

One group of 10 plus 1 is 1, 1, 11.

One group of 10 plus 2 is 1, 2, 12.

plus 3, 13.

Now we shall make a jump of 3, 14, 15, 16, and another jump of 3, 17, 18, 19.

What's next? We don't have any more digits.

We have two groups of 10, 20.

With a jump of 5, we have 2 groups of 10 plus 5, 25 with another jump of 5 we have a new group of 10, 30, 3 groups of 10. And now we shall do a jump of 30.

So we add 3 groups of 10 we have 6 groups of 10, 60.

With another jump of 30, we have 90, 9 groups of 10.

And then we add units 91, 92, 93, 94, 95, 96, 97, 98, 99.

And then we don't have any more groups of 10.

We have a group of 10 groups of 10, 100.

Let's try with a bigger number, 256.

2 groups of groups of 10, 5 groups of 10, 6 units.

And now let's go further with Python.

Lauch Anaconda and Spyder and follow me.

We shall first display numbers, starting with 1, print 1, and we display 1.

We continue the counting.

print 2, and it displays 2.

And then print 3, the next number, and it displays 3.

Now we shall print the five first digits into a list into brackets: 1, 2, 3, 4, 5.

And we have the five first digits into brackets.

But this is tedious so to repeat an action.

We make a loop.

for i in range of 1, it starts from 1, to 11, and it goes to 10 because 11 is not included.

double point, print i.

And it will display all the numbers from 1 to 10.

That's it! Now we will redo it, but starting from 10 to 100, so we type 101. And we don't want to have all the numbers.

So we make an interval of 10.

So we have the numbers from 1 to 100 by steps of 10.

We continue.

Starting from 100, going to 1000, 1001, by steps of 100.

And we have the numbers from 100 to 1000 by steps of 100.

We could continue like that a very long time.

What's coming now? What's coming now is continue counting How far? Up to infinity?