How much would the mathematical system change if one more number was added?

Answer 1

Suppose you were to add a new number to mathematics, let's call it n. To be truly part of mathematics, you'd need to have a way to add it to other numbers. So you'd have to have n+1, for instance. This can't just be n, because if n+1=n, you could cancel the n from both sides and get 1=0. It can't be one of the previous numbers in mathematics, because then n would that number -1, which would be an old number, and we said n was new. So it would have to be another new number! If you keep going with this idea, you'll see you'd have to add infinitely many new numbers n+2,n+3,...

What's next? You'd have to be able to multiply n by all the old numbers, and all the new ones too! What about square roots?
All this means you can't just add one number, if you want to do mathematics.

By the way, there are ways to get bigger and bigger number systems: you should read about complex numbers, quaternions, octonions, sedenions, etc. for examples.

Answer 2

Basically the standard numbering system is the "decimal system" (10-digit system) composed of the digits
0
1
2
3
4
5
6
7
8
9
and we count as 1 2 3 4 5 6 7 8 9 10 11 12 13 14 etc.

but if you were to add another digit, say the digit A (commonly) the system would be
0
1
2
3
4
5
6
7
8
9
A
and we would count as 1 2 3 4 5 6 7 8 9 A 10 11 12 13 14 15 16 17 18 19 1A 20 21, etc.
This is the 11-digit system (the base-11 system).

In fact there are many digit systems (like binary, octal, hexadecimal, base-3, base-4, etc), it is just that we only use decimal.

Mathematical operations and constants can be converted from one number base system to another.

^_^

Answer 3

its in its absolute...not another digit which is not there can be added to the series 1 2 3 4 5 6 7 8 9 0 if adding one digit is what you mean. if you want to add a number to any number, you can go on adding forever...changes nothing coz the numbers already exist...problem is where those numbers end.

Answer 4

hmm... we do have examples where more than 10 numbers are used for counting, eg: hexadecimal system, or where less than 10 numbers are used, eg: octal or binary
The premise of mathematics is such that it applies to all notations without worrying about which system is used.

However, the problems are in making those systems talk to each other. If you wanted to make a calculator that could handle those 11 numbers, you would need to do a lot of modifications in software and handware to do so.
if you wanted to be able to convert from this 11 digit representation to decimal, you would need to do some work as well..

Answer 5

Not much. Mathematics has no problems dealing with base 11, or base 16, or binary equations or values.

You'd end up with a lot of confused and unhappy people, however, because although math can handle any base, we older humans are trained in base 10, and learning that was hard enough.

Answer 6

. . n+1
10

Answer 7

jst like adding another letter to an equation instead of 1x+2= 12
you get 1x + c +2 = 12
meh

Answer 8

infinite changes