Let's invent some new math!!!

[Phil P]

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!!!

[pensive_pilgrim]

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

Seems to me like f(x)=0, unless I'm missing something.

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?

I guess you could do that but wouldn't the parallel axes always be linearly dependent on each other and thus kinda uninteresting? And two axes that were not parallel could always describe a two-dimensional system, I think, but without them being orthogonal it just wouldn't be as convenient for the typical function of two variables. I'm sure those have uses but I didn't take enough linear algebra to know off the top of my head.

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

What if there were four simultaneous 24-hour days in a single rotation of earth?

[Phil P]

Seems to me like f(x)=0, unless I'm missing something.

Yea it would, they would add to zero. If you just had the positive values, it would be a y-axis in the positive though.

I guess you could do that but wouldn't the parallel axes always be linearly dependent on each other and thus kinda uninteresting? And two axes that were not parallel could always describe a two-dimensional system, I think, but without them being orthogonal it just wouldn't be as convenient for the typical function of two variables. I'm sure those have uses but I didn't take enough linear algebra to know off the top of my head.

If the z parallel axises was dependent upon the x axis, then it would just be a function of x, correct? But what if the z axis wasn't dependent?

What if there were four simultaneous 24-hour days in a single rotation of earth?

I'm confused.