1. What does the cantor argument show?

2. What binary string corresponds to always going left as you follow a branching path down towards the fingertips of the artist in the blue castle?

3. What binary string corresponds to alternately going left and then right as you follow a branching path down towards the fingertips of the artist in the blue castle?

4.What does the Cantor Diagonal Argument show?

Are No and the same size? BINARY STRING is a way of coloring the counting numbers black or white. You can picture an infinite row of colored boxes: row o row 1 row 2 row 3 row 4 row 5 row 6 row 7 00o 0 1 2 3 4 5 I can't draw the whole thing for you, but this example is meant to suggest that the even numbers are colored black and the odd ones white. Of course, there might not be any pattern at all in a binary string If the answer were yes, then we could record the bijection in a chart like the one here. Row 0 shows the binary string matched to 0, and so on. Ican't draw the whole thing, of course, but 0 every binary string appears on some row of the chart. is the name of the set of all binary strings Reverse all the colors on the diagonal string, and call the new string "Bob row 0 row 1 row 2 row 3 row 4 row 5 Bob can't be in row 0 because he doesn't match in column 0. Bob can't be in row 1 because he doesn't match in column 1 Bob can't be in row 2 because he doesn't match in column 2. And so on. Therefore... Imagine walking down the diagonal of the chart and recording the colors you see BOB IS NOT A ROW ON THE CHART