>>11482093>>11482856>>11482954The cardinality of is the equivalence class of under the equivalence relation "equal cardinalities" (the existence of bijections).
>>11482214There is no such thing as "a number", but you are correct that infinity is not a real number.
>>11482259>Infinity is just a placeholder for the concept “without end” or “gets larger and larger.”This is only somewhat correct in the sense of analysis, where the symbol comes up in limit notation as syntactic sugar, but even then, limits are actually rigorously defined. is just fancy notation for the formal statement where is a positive real number and a positive natural number, and is just fancy notation for the formal statement where is a positive natural number and a positive real number. (In fact, for that second statement, it is more accurate to just say " is undefined.")
In the sense of set theory, which is what people are actually talking about when they talk about "infinities" (cardinalities of infinite sets), you are incorrect. "Infinity" here is a cardinal number, usually , but NEVER EVER .
>>11482873Brainlet.
>>11482950>It helps us escape from the fact that there's a number bigger than Graham's Number.There are uncountably infinitely many real numbers greater than Graham's number.
>infinities are just mathematical concepts and don't really have much meaning in our universe.Define "meaning."
>>11482991>Define "number"No such thing. Cardinal numbers exist, however, and are rigorously defined.
>"element" and "set"Depends on your axioms.
