It blew my mind when someone explained to me how some sets of infinity numbers can be infinite yet still technically larger than other sets, like the set of all numbers vs. the set of all odd numbers.
Yes that’s right, but I’d like to clarify that if we’re talking about whole numbers then my understanding is that the set of all whole numbers is the same “size” as the set of all odd numbers. The quick and dirty way to think about it is you could theoretically make a list of all the odd numbers and all the whole numbers and assign each whole number to an odd number at a 1-1 ratio
The reason the set of all numbers is “bigger” is because of things like fractions and irrational numbers. Try assigning an odd number to every decimal. You can’t even make a list of all the decimals. There is no non-zero interval between which a finite amount of decimals exist.
It blew my mind when someone explained to me how some sets of infinity numbers can be infinite yet still technically larger than other sets, like the set of all numbers vs. the set of all odd numbers.
Yes that’s right, but I’d like to clarify that if we’re talking about whole numbers then my understanding is that the set of all whole numbers is the same “size” as the set of all odd numbers. The quick and dirty way to think about it is you could theoretically make a list of all the odd numbers and all the whole numbers and assign each whole number to an odd number at a 1-1 ratio
The reason the set of all numbers is “bigger” is because of things like fractions and irrational numbers. Try assigning an odd number to every decimal. You can’t even make a list of all the decimals. There is no non-zero interval between which a finite amount of decimals exist.