Cz: "Peegee" is a valid number

[Peegee]

well he didn't say it verbatim but he'll concede that he invented the notion and agrees with my claim.

Here goes.

A number is loosely defined as a permutation of any amount of digits from the set [0-9]. It can also be associated with an english word, so that when you see the english word 'Three' you know it means '3'.

An english word for any number is defined as a permutation of any amount of characters from the set [a-z]. We could specify something like how a vowel must exist in the word, and since english words technically don't have a maximum length, it would just be another infinite set.

Now, we have two infinite sets. Like two lines with infinite dots, one can draw a 1:1 association between each number and each word. You'd run out of 'numbery' sounding words eventually, and will have to start using other permutations of the english alphabet. Eventually you'll run out of unique words, and have to 're-use' words, like the word 'word', or the word 'peegee', or 'seazy', etc.

Ergo, Rye, ryechu, pikachu, peegee, microphone, and camera are all numbers.

Thanks to Cz for hurting my head. >: (

[rubah]

are you drunk peegies

or high?

[mulley]Maybe in France they allow that sissy double posting stuff, but not 'round these parts! [/mulley]

[Peegee]

No double poasting.

I'm neither.

[Lawr]

I like cake.

[Peegee]

I like cake.

cake and sagensyg would be numbers in my argument.

[Denmark]

Why have I always perfectly understood you, PG?

Bonus: TRANSLATE THAT INTO NUMBERS!

[Lawr]

I think I get it, like the number '17039' has no repeated numbers. And 'Person' has no repeated letters. Is that right? Or are you on some mushrooms or something?

[rubah]

mullet, if you can't recognize an excellent example of double posting, i don't know if I want to be your friend anymore.

denffe is the number 491508 or 049158 or something.

holy crap I can't believe I just did that.

[Cz]

See, I told you this was too deep for GC.

[Peegee]

No I'm just poor at expressing myself properly.

Every number as an associated english word . one, two, three, four, seventy, sixty seven million, etc.

I'm arguing that since numbers are infinite, there must be an infinite amount of words to describe them. Since an infinite amount of things, where the thing is just any permutation of a finite set will just exhaust new/made up items in that set (like made up words for numbers) we'll have to use items in that set that we understand as other words, such as peegee and apple.

[Lawr]

Ok I get you. So you're taking the stand point from the term "Googol" meaning 100 zeros. Sagensyg will be a number and 450 zeros after it.

[Peegee]

Ok I get you. So you're taking the stand point from the term "Googol" meaning 100 zeros. Sagensyg will be a number and 450 zeros after it.

Right, except you aren't defined yet, but you and every other possible english word theoretically has a number attached to it.

[rubah]

just say 'every number has a name'

sag just defined himself, i think.

[Peegee]

just say 'every number has a name'

sag just defined himself, i think.

It's not official yet.

[o_O]

well he didn't say it verbatim but he'll concede that he invented the notion and agrees with my claim.

Here goes.

A number is loosely defined as a permutation of any amount of digits from the set [0-9]. It can also be associated with an english word, so that when you see the english word 'Three' you know it means '3'.

An english word for any number is defined as a permutation of any amount of characters from the set [a-z]. We could specify something like how a vowel must exist in the word, and since english words technically don't have a maximum length, it would just be another infinite set.

Now, we have two infinite sets. Like two lines with infinite dots, one can draw a 1:1 association between each number and each word. You'd run out of 'numbery' sounding words eventually, and will have to start using other permutations of the english alphabet. Eventually you'll run out of unique words, and have to 're-use' words, like the word 'word', or the word 'peegee', or 'seazy', etc.

Ergo, Rye, ryechu, pikachu, peegee, microphone, and camera are all numbers.

Thanks to Cz for hurting my head. >: (

Whether or not you run out of words depends upon whether or not you apply a set constraints to the selection of a word, such that a situation arises whereby there cannot be a valid name derived from existing ones. For example, if you said that a name is only valid provided that it doesn't contain a repeated string of two or more characters, you can easily see that there is a limited number of names you may choose. You can visualise it like this:

Take some alphabet of arbitrary size (we'll use 2, for argument's sake) = { A, B }.
Any number name can be created from this alphabet, but you can't have a two-character string repeated.
Now you take the set of all possible names - to speed things up I'll give examples by word length:
1: A
2: AA
3: AAA
4: AAAB
5: AAABB
6: AAABBA
7: AAABBBA
8: I challenge you to come up with an 8-letter one.

Mathematically, if you visualise each character of the alphabet as a state, as you sequentially read each letter of some string, there can be at most <i>n</i> state changes for an alphabet of size <i>n</i> before a repeat of a two digit string is inevitable. Similarly, if you restrict yourself to say <i>actual</i> English words, you only have 30,000 or so different numbers you can name.

If there are no such restrictions then there is an unlimited number of names. The proof is trivial: For word length <i>n</i> append character at posi<b></b>tion <i>n-1</i> to string. In other words, you simply append the same character over and over. For an alphabet of size <i>m</i> and some arbitrary word length <i>n</i>, the total number of unique names is <i>mⁿ</i>; since there is no limit on the number of letters in a word, every word length is valid, and the number of words rapidly increases in magnitude with word length. Therefore, for our English alphabet there is <i>26ⁿ</i> for all possible word lengths <i>n > 0</i>.