Not a book for those with significant formal training in mathematics - y'all will know it all already. But for me, I found Alex Bellos's book Alex's Adventures in Numberland an amusing read (Bloomsbury, ISBN 978-0-7475-9716-2).

I also knew quite a bit of the subject matter, but it didn't stop it being an enjoyable read, and it brought home to me how much more interesting "pairs of numbers" might be than simply "interesting numbers".

For example, who would have thought that

2592

and

24547284284866560000000000

would make an "interesting pair"?

[EDIT] Actually, having Googled the larger number, I find that it is really pretty boring. There are another 10 numbers in the set, being the integers in the range 0 to 9 inclusive.

Page 1 of 1

## Interesting numbers Really a book recommendation

### #1

Posted 2011-March-03, 00:43

Psych (pron. saik): A gross and deliberate misstatement of honour strength and/or suit length. Expressly permitted under Law 73E but forbidden contrary to that law by Acol club tourneys.

Psyche (pron. sahy-kee): The human soul, spirit or mind (derived, personification thereof, beloved of Eros, Greek myth).

Masterminding (pron. mstr-mnding) tr. v. - Any bid made by bridge player with which partner disagrees.

"Gentlemen, when the barrage lifts." 9th battalion, King's own Yorkshire light infantry,

2000 years earlier: "morituri te salutant"

"I will be with you, whatever". Blair to Bush, precursor to invasion of Iraq

Psyche (pron. sahy-kee): The human soul, spirit or mind (derived, personification thereof, beloved of Eros, Greek myth).

Masterminding (pron. mstr-mnding) tr. v. - Any bid made by bridge player with which partner disagrees.

"Gentlemen, when the barrage lifts." 9th battalion, King's own Yorkshire light infantry,

2000 years earlier: "morituri te salutant"

"I will be with you, whatever". Blair to Bush, precursor to invasion of Iraq

### #2

Posted 2011-March-04, 06:32

24547284284866560000000000 wow.

... and I can prove it with my usual, flawless logic.

George Carlin

George Carlin

### #3

Posted 2011-March-04, 08:10

I may get this book! Is that sick or what?

I have told my wife she may not see me for a while, I am off on a quest for indestructible numbers in base 12.

I have told my wife she may not see me for a while, I am off on a quest for indestructible numbers in base 12.

Ken

### #4

Posted 2011-March-04, 15:53

As it can be proven that all integers are interesting, I would assume the book is rather heavy...

(just kidding, I read the book when I was a student and didn't break my back in the process)

P.S. The proof: Let 0,1,2,... be denoted as the natural numbers. Zero has the property that it is the smallest natural number, so it is interesting. Then suppose n > 0 is the smallest uninteresting number. As this would be an interesting property, we have a contradiction. Ergo all natural numbers are interesting.

Extension to integers: Consider the same logic applied to the sequence 0, 1, -1, 2, -2, 3, -3, ...

Home exercise: Prove that all rational numbers are interesting.

(just kidding, I read the book when I was a student and didn't break my back in the process)

P.S. The proof: Let 0,1,2,... be denoted as the natural numbers. Zero has the property that it is the smallest natural number, so it is interesting. Then suppose n > 0 is the smallest uninteresting number. As this would be an interesting property, we have a contradiction. Ergo all natural numbers are interesting.

Extension to integers: Consider the same logic applied to the sequence 0, 1, -1, 2, -2, 3, -3, ...

Home exercise: Prove that all rational numbers are interesting.

### #5

Posted 2011-March-04, 16:55

Incidentally, there are other indestructible numbers (e.g., 9225 or 92251). The author of this book has things incorrect, slightly.

The actual conjecture of Sloane is that 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2592, 24547284284866560000000000 are the only fixed points of the powertrain map (A point x is fixed by a map F if F(x)=x).

I have not seen it in print, but it may also be a conjecture that every integer other than those above has a fixed point in its orbit:

that is: in the set {x, F(x), F(F(x)), F(F(F(x))), ...} one of the above numbers always comes up.

Note that it's not immediately obvious that there aren't distinct x & y, such that F(x) = y and F(y) = x.

Nor is it obvious (to me) that there aren't distinct x, y, z such that F(x) = y, F(y) = z, and F(z) = x.

[Maybe it is clear, but I haven't thought about it]

The actual conjecture of Sloane is that 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2592, 24547284284866560000000000 are the only fixed points of the powertrain map (A point x is fixed by a map F if F(x)=x).

I have not seen it in print, but it may also be a conjecture that every integer other than those above has a fixed point in its orbit:

that is: in the set {x, F(x), F(F(x)), F(F(F(x))), ...} one of the above numbers always comes up.

Note that it's not immediately obvious that there aren't distinct x & y, such that F(x) = y and F(y) = x.

Nor is it obvious (to me) that there aren't distinct x, y, z such that F(x) = y, F(y) = z, and F(z) = x.

[Maybe it is clear, but I haven't thought about it]

"I think maybe so and so was caught cheating but maybe I don't have the names right". Sure, and I think maybe your mother .... Oh yeah, that was someone else maybe. -- kenberg

"...we live off being battle-scarred veterans who manage to hate our opponents slightly more than we hate each other. -- Hamman, re: Wolff

"...we live off being battle-scarred veterans who manage to hate our opponents slightly more than we hate each other. -- Hamman, re: Wolff

### Share this topic:

Page 1 of 1