This is the first of at least two posts I feel I must write to explain concepts I want to use in future posts, for future problems and ideas. A fairly basic, but necessary post that will allow bigger and better things to come. Linear Algebra, I’m coming for -you!-
Most people have an inherent sense of numbers. Quantities you can add, subtract, multiply, divide. 2 + 2 is always 4, and so it goes. Some may visualize a line of numbers extending off to infinity, with an inherent order. Some may even think of the set of numbers. However you think of it, most people have some idea of how numbers work.
Interestingly, Mathematics, and many Mathematicians, function in a parallel world, at a glance not too unlike our own, but certainly different. 2 + 2 does not necessarily equal 4, because there may not even be a 4 to equal, let alone 2’s to add. Numbers are no longer quantities, but shapeless objects, capable of interacting with each other, but little else.
But it is those interactions that make them worthwhile.
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