Perform mathematical calculations like addition

[kiru]

My question seems to be so idiotic.please forgive me for that.On what basis we perform mathematical calculations like addition and subtraction?As for as decimal system is concerned we have only 10 uncontinuos digits.but we are doing so much magic(I don't know whether I am using the correct word)with them.I am amazed.

 

[JasonRox]

I believe the study of mathematics has very little to do with our number system.

We (or atleast I) don't think much of numbers 1 to 10 when writing proofs, and theorems.

 

[abdo375]

Explain your question

 

[kiru]

We use digits starting from 0 to 9 and then repeat the same numbers by adding prefix from the numbers that we know but in a proper manner.In practice If there where ten balls, in decimal system it is represented by 10 .Is it a mere encodification?I feel difficult when I use Hex integers where we use 0-9&A-F.Why can't we have some other means of numbering?

 

[Gokul43201]

You can use any number (2 and up) as a base to represent any real number. Nothing terribly special about 10.

 

[neurocomp2003]

the decimal system is just our language reference( ibelieve in in history its associated with our digits on our hands/feet)...int comptuer world you deal with binary,octs,hexs. I believe some researchers are trying to work on a tertiary system.
The reason we use binar/ocs/hex is because of the powers of 2...binary being the simplest system for a computer...

now if your talking about language theory(compsci/math) ...then the digits are our alphabet like goku said...and you can have as many digits in the alphabet.
and then you string them up to make a word(in this case a number)...now from settheory(and i think predicate calc/ or turing machines...the one that studies pred/succ)...your words follow an order(counting order and they must be sequenced because the number system represents counting) so in binary {0 1 10 11 etc.} and in decimals you get { 0 1 2 ..9, 10 etc}...each time you add an extra letter to the word its because you ran outta counting room...but remember you can't add new letters to the alphabet you can use only preexisting ones. so the sensible thing is to add the next letter infront fo the previous word. By all means I'm sure you could make a new system wher eyou add 2 letters to the front...but addign one ist he simplest.

And note that all these different number systems are bijections between each other because they are 1-1 & ONTO.