and also ELI16 what a an imaginary number is and how it works in real life
In: Mathematics
Lots of great answers!
I’d like to offer a different approach. “What is a number anyways?” Seriously.
How do we know that when I write “2” you and I both know what this means?
– Because of rules.
If two objects follow the same rules exactly – then they are the same. Easy enough, so we think…
Answer me this: “what comes after 2?”
If you’re dealing with only natural numbers, whole numbers or integers – the answer is “3”. Perfect.
If you’re dealing with irrational numbers (like 2.1, 2.01, sqrt(2), pi, 7, etc) then the answer is …. There is no answer. Uh oh!!
The concept of “what number comes after a number” is totally invalid with irrationals. It’s not 3, it’s not 2.5, it’s not 2.0000000001, and there no such number of “2.000-infinitely-many-0s-then-1” because infinite implies no end so there can never be a 1.
Therefore “2” in irrational numbers is a totally different object from the one in integers. Woh man.
So this is a long post to illustrate that numbers are objects that follow rules. And if we want to solve some problems in the world, we have found that allowing sqrt(-1) = i to be a very handy thing indeed!
In short – it simplifies anything that oscillates or rotates. Which is a lot of what goes on in machines and electromagnetic waves.
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