Why a Proper Number System is Important in Mathematics

A proper numbering system in mathematics is a very important part of being able to do math.  We might be able to do algebra using letters, but without the numbers these letters are meaningless.  The numbers themselves might start off as arbitrary but they do gain value once it is figured out how they work.  A simple number system can make predicting how the world will react to different things possible.  Trying to do complex math with roman numerals sounds to cumbersome to even attempt.  A simple number system can even make learning math easier, while a complex numbering system would make it difficult to grasp the more complex parts of mathematics.

In mathematics numbers act as placeholders in an arbitrary way.  They are arbitrary in the sense that at one point someone said this squiggle line is worth more than that squiggle line.  This holds true for the numbers 0-9 and then the numbers have a pattern that they follow.  Without these placeholders doing math would be impossible it would lead to statements like finding the derivative of that big number multiplied by that slightly smaller number.

Having placeholders in math is important, but it also matters how easy the placeholders are to work with.  Using a cumbersome number system like roman numerals would make doing math significantly more difficult.  Trying to do even simple division with roman numerals would take an incredibly long time.

It has been shown that places with simpler number systems tend to have better test scores than countries with a complicated numbering system.  Students in China have an easier time learning math because instead of having eleven their number translates closer to one-ten which would make learning how to count in the teens easier.

So while the shape of the numbers might not be important, how easy they are to use and the fact they exist is very important.  The easier the numbering system itself is the easier it will be to learn and the more complex the math can be that uses the numbering system.

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