So, Noneuclid decided to break one of Euclid's 5 rules of geometry, and he came up with noneuclidian geometry. Cool. I've always wanted to do something like that.

Acow, your blog reignited that spark of imagination in this topic. Is there avenues of mathematics that have been ignored because no ones tried them before?

Here's some of my speculations:

Let f(x) = 2x + 3

Then f(2x) = ? If f(2x) = 2(2x + 3), then f(2x) is simply 2f(x).

And f(sinx) = ?

And f(x+y) = ?

And f(x^y) = ?

Then there's this one:

Does f(x) = |infinity*x| + -|infinity*x| = a y-axis at that x value?

And what if you had a graphing system with xyz where x and z were parallel to each other and y was perpendicular to them? And what if you just had an xy system where x and y were parallel to each other? And what if x and y were neither parallel nor perpendicular?

And what if we had five directions on planet earth instead of four?

Lets all think of some more problems like this and try to answer each others!!!

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