[bradwood]

Infinity times infinity equals a bigger infinity

[anikan_vader]

Do you have an example of when this is true? It is certainly not true of integers, or rationals, or real numbers. Typically the Cartesian product of an infinite set with itself is bijective with the original set.

[bradwood]

mathematical intuition? positive numbers when multiplied together always equal numbers larger than either of the multiplicands...

hardly a rigorous proof, I grant you, but surely true?

[r0uv3n]

In fact, the opposite of your statement is true: Assuming the axiom of choice, the cardinality of the product X^2 of some infinite set X is always the same as X.

See https://math.stackexchange.com/a/2464655 for a quick proof