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Set Theory and Logic


Well-Known Member
The Set Theory of Cantor

Cardinality - Wikipedia

says: the cardinality of the infinite amount of real numbers between 0 and 4 is more than the cardinality of all natural numbers 1,2,3,4,5,...., infinity.

However, if we say: "amount of numbers between 0 and 4", then we are using discrete language, not the continuous one.

That means that we assign each number from the gap 0..4 the ordering number, for example, 1.23456= 34, 2.678= 56, Pi = 45.

Therefore, the cardinality of the sets is the same: we can list all real numbers from 0..4 using natural integers.