00:01
Okay, so we want to show that any two intervals, a, b and c, d have equal cardinality.
00:06
To do this, we're going to find a bijection f, which maps a, b, to c, d.
00:12
So any bijection will do, but we're going to try and find the easiest one.
00:15
In particular, what we're going to do, if we take the x, y plane like this, let's suppose a is here, b is here, and c and d are here on the x, y plane.
00:27
Well, we're going to try and find a mapping from the interval, a, b to the interval c, d, which is just a straight line.
00:35
So if we have this point here and we have this point here, then we want to find an equation of a line which joins these two points.
00:48
And clearly, if we do this, we're going to have a bijection from this interval to this interval...