/sci/ - Science & Math

what is a number?

i know we numerals like 1,2,3,4,5,6,7,8,9,0, but what are they representing?

why is it that when we add numbers their order doesn't matter, and when we multiply by 1 or add by 0 the original number is the same?

what gives them such properties?

this shit has always eluded me even while doing algebra work. i don't like just computing shit when i don't even know what i'm moving around, especially when dealing with commutativity and that units can be preserved (1km +1km = 2km, 2x2km=km^2).


why? what causes/does/IS this? is there anything to encapsulate this in some theorem? or is it just the way it is and we have to just treat it self evident?

What is the smallest number that cannot be described in less than twelve English words?

There's got to be one, since there are only a finite number of English words and a finite set of twelve english words cannot be mapped to an infinite set of all numbers right?

1/n is generating (in base n) the number 0.111...

Step by step it builds up like this: 0; 0,1; 0,11; ...

Does this mean the set of all finite numbers like 0 and 0,1 and 0,11 and so on is equal to 1/n ?

Is it possible to create a language with only numbers,no punctuation,that can be translated to English?If yes,what is the most effective way of doing it and to translate it?