We never did resolve the question of which grows faster:
In this corner we have
Sequence 1 n^^n
1, 2^2, 3^3^3, 4^4^4^4, and so on.
And over here we have Sequence 2, defined recursively by
In short, we can define the second sequence as s(1) = 1; s(n) = n, followed by s(n-1) factorial signs.
Which sequence grows faster than the other??
We have many conflicting answers, and no decisive resolution; here was one idea .
Our minds boggle as we continue our quest! This week we discuss the Knuth Arrow notation, for describing some really staggeringly large numbers. And yet we are still two weeks from talking about the largest number ever used for any real purpose!
We also discuss an April Fool’s paradox! Last week we said there were three errors on the Math Factor. But there were only two, so this announcement was one of the three errors! But then the announcement was correct! ETC.
We’re well on our way towards describing the two largest numbers that have ever been used! Unfortunately, there are at least three errors in this segment of the Math Factor–can you spot them all?
David R. of Palo Alto writes:
Have you ever discussed factorials on your podcast? I don’t recall,
but a friend and I are puzzled and so of course we turn to you: Why
is “zero factorial” 1? Was it simply defined that way to frustrate
all of us nonmath folks, or is there a valid explanation?
We discuss the results of the fabulous Math Factor Million Dollar Giveaway. and confess this was an excuse to bring up Game Theory and how to talk about really big numbers.
The solution to the cake cutting puzzle; the end of the Million Dollar Give-Away.
We take this week off to celebrate Pi Day (March 1)
Ok, that’s only π to one decimal place, and only in some countries, but somehow we got off a week in our radio version of the Math Factor and have to catch up.
How to satisfy the most jealous of triplets?
Twenty three people split into two teams of eleven & one ref; no matter how they split, the teams have the same total weight! Can the players themselves be different weights?
A short, but tricky puzzle: how many guests must you invite before you can be sure that there are at least three mutual acquaintances or three mutual strangers?
Download a great math factor poster to print and share!
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