Re: 1 to 10

William Elliot writes:
On Fri, 30 May 2008, David R Tribble wrote:
2048 = (1 + 1)^11
oo = 11^11

Surely that last line is a typo?

Not at all. It's the biggest four 1 number of all. ;-)

Surely 11!^11 is bigger. And 11^11!. And 11!^11!. How about 1111!, or
11!11!.

How many rational four 1 numbers are there?
Is there an irrational four 1 number? Yes, several.
.1^(1/(1 + 1))
1.1 ^ 1.1

A number is four 1 when it can be expressed by
any number of + - * / ^ . ! and four 1's.

Four 1's can be exactly or atmost. It'll make no difference.

How many four 1 numbers are there?

That ! has been underused so far, I think. You seem to allow
parentheses: 1111!, (1111!)!, ((1111!)!)!, and so on. No biggest.
.

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