One small doubt

[Arushi :))]

For an experiment on flipping a coin until a head appears,
S = {H, TH, TTH, TTTH, TTTTH,......}
But even here the number of elements can be matched one-to-one with whole numbers, and in this sense the sample space is said to be countable.
If a sample space contains a finite number of elements or an infinite though countable number of elements, it is said to be discrete.
What does it exactly mean?

[Sinistral]

A set is said to be finite if it has finite number of elements. Clearly a finite set is countable.
A set X may contain infinite number of elements but still it may be countable if there exists a bijection between X and the set of natural numbers (N). In other words X is "numerically equivalent" to N. Such a set is called countably infinite set or a denumerable set. for example a set of even numbers is denumerable.
X={2n: n ∈  N}. Clearly there is a bijection between X and N.

In ur case set S = {H, TH, TTH, TTTH, TTTTH, . . .} has a bijection from S to N.
So S is denumerable and by definition discrete.
The author of the book (which u r following) used whole number set instead of natural numbers, but that doesnt make any difference in the definitions.
The author defined a set to be discrete if it countable. So S is a discrete set.

To Sum up: A countable set can be either finite or denumerable.
The set containing all real numbers or the set containing all irrational numbers is clearly infinite.

Arushi :) wrote

For an experiment on flipping a coin until a head appears,
S = {H, TH, TTH, TTTH, TTTTH,......}
But even here the number of elements can be matched one-to-one with whole numbers, and in this sense the sample space is said to be countable.
If a sample space contains a finite number of elements or an infinite though countable number of elements, it is said to be discrete.
What does it exactly mean?

[Arushi :))]

Thanks buddy