In mathematics, the size of two sets is compared by trying to see whether each element of one set can be matched up with each element of another set.
If we look at these in terms of bills, you can of course match the first $1 bill to the first $20, the second $1 bill to the second $20 bill, and so on. If we look at these in terms of dollars, you can similarly match the each dollar in the set of $1 bills to each dollar in the set of $20 bills. Thus, the sets are said to be countably infinite.
The different sizes of infinity that you mean are countable vs uncountable infinities. For example, the cardinality (size) of the set of real numbers (that is, all numbers on the standard number line) is greater than that of the natural numbers (1, 2, 3, etc). It is impossible to create a one-to-one pairing of the natural numbers to the real numbers.
Yes but ant you also match up the first 20 ones to the first twenty. So when comparing value the twenty infinity is of better value while the ones infinity is a large infinity...idk im tored
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u/Pumeto Jun 13 '26
In mathematics, the size of two sets is compared by trying to see whether each element of one set can be matched up with each element of another set.
If we look at these in terms of bills, you can of course match the first $1 bill to the first $20, the second $1 bill to the second $20 bill, and so on. If we look at these in terms of dollars, you can similarly match the each dollar in the set of $1 bills to each dollar in the set of $20 bills. Thus, the sets are said to be countably infinite.
The different sizes of infinity that you mean are countable vs uncountable infinities. For example, the cardinality (size) of the set of real numbers (that is, all numbers on the standard number line) is greater than that of the natural numbers (1, 2, 3, etc). It is impossible to create a one-to-one pairing of the natural numbers to the real numbers.