You say that 0.00...0001 is finite.
How can you call 0.00...0001 and 0.11...1111 infinite??
the former is the representation of product(i=1,infinite) of 1/(10^i) = 1/10 * 1/100 * 1/1000 * ...
and the later is the representation of sum (i = 1, infinity) of 1/10^i = 1/10 + 1/100 + 1/1000 + ... = 0.(1)
The former might be written 0.(0)1 but I guess this is not allowed to be written. Anyway, you can't find a number smaller than it because there are an infinite number of decimals (which mean, an infinite number of "0" decimals, all before that "1").
How can you call 0.00...0001 and 0.11...1111 infinite??
the former is the representation of product(i=1,infinite) of 1/(10^i) = 1/10 * 1/100 * 1/1000 * ...
and the later is the representation of sum (i = 1, infinity) of 1/10^i = 1/10 + 1/100 + 1/1000 + ... = 0.(1)
The former might be written 0.(0)1 but I guess this is not allowed to be written. Anyway, you can't find a number smaller than it because there are an infinite number of decimals (which mean, an infinite number of "0" decimals, all before that "1").
