If we start counting at zero, and stop when we get to 9, how many numbers have we counted?
That's 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
The answer isn't 9, is it? It's ten. That's because we started at zero, not at one.
If we counted from 0 to 99, how many numbers would we have counted? It's not 99 - it's 100. (Because we're counting from zero again.)
In the same way, if we count from 0 to 9,999, how many numbers do we count? The answer is 10,000 - not 9,999 - because we've got to remember to count the zero.
If we wanted to write down all the telephone numbers that we could think of that have 4 digits, we could start writing at 0000, then 0001, then 0002, and so on all the way up to 9999. But that would be just like counting from 0 to 9,999. And we have just said that there are 10 thousand of these numbers.
But, hold on, we were told we couldn't begin with a zero, so we shall have to leave out all the numbers we just pretended to write down if they begin with zero. These will be all the numbers from 0000 to 0999. How many of those will there be? Well, this is just like counting numbers from 0 to 999 - and there will be one thousand of these.
So, out of our 10 thousand telephone numbers, we are not allowed to count one thousand of them, because they begin with zero. That leaves 9,000 that we are allowed to count.
How does that sound?