Are there many fewer rational numbers than reals?

analysis real-numbers

Intuitively, think that the rational numbers have a periodic decimal representation. If you draw a number digit by digit, what are your chances to make a periodic drawing compared to a completely random one ?


All of the answers here presume that your [0, 1] denotes a subset of the Real Numbers, but you said,

Well, this lesson is called "Introduction to Computers"

Computers do not use Real Numbers. If [0, 1] denotes the set of numbers that could be returned by a random number generator (procedure) in a computer program, then the probability of getting a rational result from it is 1.

Every floating-point number is rational.

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