Intro to definitions
After talking on more phylosopihcal ideas about math in What is Math? Why Math? and infinity.
Lets start being PRACTICAL.
Why do I start practice with definitions?
Like the linux old saying "linux is failes and files are everything".
The same with definition - math is definitions and definitions are everything.
So math seems pretty easy now :)
But, as said, defintions are everything, so we need to definie what do I mean by defintions, and how do I use those defintions.
In the post on infinity we already defined infinity.
Its wasn't easy, or that clear, and anyway, no matter what you define, to make it part of the mathematical system you have to agree on some basic rules.
What are the rules?
I don't know.
I know when I am clearly inside them, I know when I am clearly out of them,
but when I am in the grey area, I make mistakes... so, I really don't know.
Most of the times definitions are built on other definitions, so step by step, defintion built on another, math can become very complex....
Example
Lets take limit of a series as an example.
The series is 1n.
The limit is defined as the number this series is approaching to as n going to infinity
The way to write it in math is:
