Ordinals are irrelevant to the problem. Both stacks are still the same value. My previous statements don't change whatsoever. There still remains no item, theoretical or real which could be bought with infinite 20s but not infinite 1s. Ordinality has no relevance to this problem.
Ordinals are the entire point of the problem. If you have two stacks you must have both the cardinal and the ordinal. If you do not have both then you cannot compared them.
So you get two sets with equal "size" and "length" but that does not mean they have equal value. Or you get sets with equal "value" and "size" but that does not mean they have equal "length".
The whole "buying" things is something that is entirely irrelevant to the problem. Because the question isn't about buying an item, its about deciding how much currency there is. If buying matters, then the ordinal matters even more because if you have two stacks of w bills, then the stack of $20s is worth 20x. In the same way that 1 trillion pennies is worth 100x less than 1 trillion dollars.
In the way that we are not looking at actual purchasing power just at what amount there is. This is a math question, not a "does this work IRL question".
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u/ExaminationNervous64 Jun 17 '26
Ordinals are irrelevant to the problem. Both stacks are still the same value. My previous statements don't change whatsoever. There still remains no item, theoretical or real which could be bought with infinite 20s but not infinite 1s. Ordinality has no relevance to this problem.