Mdthbs

It’s been a while since my last post since school, work, and family have kept me incredibly busy. I have another puzzle though and as always I wish you the best of luck.

Sarah called me today and explained that she had counted to infinity. I shrugged and said it was impossible. She said that since I didn’t believe her, she would do it again, and this time in only ten minutes. I thought it was impossible but she did it right before my eyes!

How did Sarah count to infinity in only ten minutes?

Clarifications

Sarah indeed counted all the way to infinity.

Perhaps

clever Sarah went the appropriate "I" page in the dictionary and counted word entries until she reached "infinity"

This feels underspecified:

clearly Sarah is not counting 1, 2, 3, ... (infinitely many numbers go here), infinity; so she's doing something else; but there are quite a lot of something-elses that she could do, and all of them are kinda cheaty, and the question here is what specific kinda-cheaty thing she did.

Here are a few possibilities. One:

She wrote numbers down on their sides, starting at 1 and proceeding as far as 8. An 8 on its side looks very much like the usual mathematical symbol for infinity.

Two:

She started from, let's say, "infinity minus 100" and counted up. (There are in fact number systems in which something a bit like "infinity minus 100" is an actual number.)

Three:

She counted down from, let's say, "infinity plus 100". (You can do something like that in the surreal numbers, mentioned above, but also in other simpler systems such as the ordinal numbers.)

Four:

She started counting normally, and at some point went "... and so on; infinity." I personally wouldn't (ahahaha) count that as counting to infinity, but then I don't think I'd count anything as counting to infinity other than the thing she obviously didn't do.

Five:

Sarah is able to count arbitrarily fast (maybe she's an archangel or something, not a human) and she said each number twice as quickly as its predecessor; after twice the time it took her to say "one", she had named all the positive integers and then said "infinity".

There goes one Infiniti G35! And there goes another!



There. I've counted two Infiniti. ;)

The definition of infinity in some circles is

the highest conceivable number.

Therefore, all Sarah needs to do is count to

the highest number she knows of, be that a hundred, a thousand, whatever. Because she cannot think of any number higher than that, that is her "infinity".