unambiguously describing a number pt.2

[BMAD]

If you equate a word to the number of its letters, what do you have?

One is three, which is five, which is four of course. So one is four.
Two is also three, which we now know to be equal to four (see above).
We know three is four and four is four. We’ve been through that.
Five is also equal to four.
Six is three, which is five, which is four.
Seven is five, which is four…
.
.
.
Twentyfive is ten, which is three. And three is five, which is four.
.
.
.
Ninehundred is eleven, which is six. And six is three. Three is five, which is four.

Even zero is four.

How about words that are not numbers?

Nothing is seven, which is five, and that leads to four.
Universe is eight, which is five, which is four.
You are three, which we now know is four.
I am one, which also boils down to four.
So you and I are four…

And if someone tells you that you and I are one, well, that’s true also, because one is three is five is four!

Well, apparently all is four.
And that is true of course because all is three, which is four.

Is there a counterexample?

[bonanova]

Looks like convergence to me....

[ParaLogic]

Wow! I was actually thinking about this exact situation a couple of weeks ago, and I noticed the same convergence.

But I didn't consider proving it...

[BMAD]

Does any of our Spanish speaking friends know if such convergence exist for Spanish numbers? I am unsure as I believe cuatro is seis and seis is cuatro making a loop. But I am not as proficient in spanish to be certain.

[ParaLogic]

uno>tres>cuatro<=>seis

dos>tres>cuatro<=>seis

cinco<=>cinco

siete>cinco<=>cinco

ocho>cuatro<=>seis

nueve>cinco<=>seis

diez>cuatro<=>seis

once, doce, trece, catorce, quince, dieciseis, diecisiete ...

So it's nowhere as neat. Numbers either end up in the 4=6 loop or at 5.

Now how about Roman Numerals?

Everything ends with I, II, or III

Edited April 14, 2013 by ParaLogic

[James33]

If we assume that this is true for the first few numbers and that the number of letters in a number is less than the number (after the first few) then applying strong induction proves that there are no counter examples.