Some Basic Questions on Decimals through Addresses

5. (c) The interval with address 0 is [0, 1/2]; the interval with address 1 is [1/2, 1]. Consequently, the addresses 01infinity and 10infinity correspond to the same point. The point with address a1a2a3 ... has coordinate

a1/21 + a2/22 + a3/23 + ...

Consequently, equating the two addresses that correspond to x = 1/2 gives

0/21 + 1/22 + 1/23 + 1/24 = 1/21 + 0/22 + 0/23 + 0/24 + ... = 1/2

This is consistent with the familiar result from geometric series

1/4 + 1/8 + 1/16 + 1/32 + ... = (1/4)(1/(1 - 1/2)) = 1/2

Return to Address questions.