Seeking help with visualizing surface

[Kmenex]

I'm a rogue babble master, hear me out.

I have been puzzled by this little idea concerning functions and the "relation" between the "size of the 1" for, say variable x, and the "size of the 1" for variable y. Naturally the two variables x and y both take "the unit" as their size of 1, and this unit has the same size in both x and y. Don't even let me mention my nonsense about "distinct sets of real numbers"

Well, what would happen if this were not the case? What would happen if the "size of 1" in the y direction was not the same as the size of 1 in the x direction? I like to describe this by saying that when x's unit = 1 then y's unit = .99998 (or something), and when y's unit = 1 then x's unit = 1.00002 ...

And then what happens when you let the difference between the units change as a function of x, or...

hmmm this isn't very well thought out.. maybe a mathematician can help me.

 

[tiny-tim]

Hi Kmenex!

We do this quite often.

For example, an aircraft measures its height in feet, but its horizontal distance in miles … that doesn't create any problems!

And degrees of laitude and longitude are of different lengths (except at the equator), and the ratio depends on where you are!