If the set is finite you count the number of distinct elements in it.
If the set has infinitely many elements, and you can find a one-to-one mapping between these elements and the natural numbers, then its cardinality is Aleph-null. Incidentally, the cardinality of rational numbers is also Aleph-null.
If you can map its elements to the set of real numbers, and if the continuum hypothesis is true then the cardinality of the set is the next transfinite number, Aleph-one. Unfortunately, if the Zermelo-Fraenkel set theory is consistent then neither the continuum hypothesis nor its negation can be proven. [It is not that nobody has proved it, but worse: as Godel proved, in any consistent and not-trivial mathematical theory, there are statements that cannot be proved to be true or false.]
To find the cardinal number of a given set, you count the number of distinct elements in that set. If the set is finite, the cardinal number is simply the total count of its elements. For infinite sets, cardinality can be described using concepts like countable and uncountable infinity. For example, the set of natural numbers has a cardinality denoted as ℵ₀ (aleph-null), while the set of real numbers has a greater cardinality.
u ask a teachr
what may be false
Deductive reasoning
The only rule for any set is that given any element [number], you should be able to determine whether or not it is a member of the set.
Count the number of distinct elements in the set.
No. The empty set has cardinal number 0. {ø } has cardinal number 1.
I feel like a better explanation is that the answer is 26. I assumed that you were asking for {x|x, as long as x is a letter of the alphabet}. The cardinal number is basically just the number of terms in the set (it has to be distinct).
instructions for cardinal 3108 digital watch
u ask a teachr
Deductive reasoning
what may be false
what may be false
what may be false
The only rule for any set is that given any element [number], you should be able to determine whether or not it is a member of the set.
Deductive
What must be true