Question

why would the domain of the surface area S of a sphere is a function of the length of an edge x be: {x|x≥0}
I thought since f(x) = 6x^2 and for a dimension to occur the length needs to be at least x>0, thus the domain should be {x|x>0}.

Answer 1

any thoughts on this one @Hero or @jim_thompson5910 ?

Answer 2

Obviously because things like length, area and volume have to be positive. Negative length, area, and volume have no meaning in terms of physical measurement.

Answer 3

so you are agreeing with me, @Hero ?
here's my input: if they are going to allow 0 in the interval, then they ought to allow negative values for x too since it is squared, which will give a positive dimension mathematically.

Answer 4

But x if x is defined as a given length, then x by default has a restriction of x > 0. Therefore, no matter what, it has to be positive.

Answer 5

in addition, zero is neither a positive nor negative.

Answer 6

alright, thank you.

Answer 7

Well, I should write \(x \ge 0\) because it is possible to describe an object that has zero length or area. However, it doesn't make sense to describe negative length of negative area.

Answer 8

you are correct, it doesn't make sense to describe negative length of any dimension to produce any geometrical area. and here's where my rationale comes in - by the same token, no geometrical shape with zero length exists.
an equation may exist, but no shape can be produced
ie x^2+y^2 +6x -2y +10 = 0 of a circle
no matter where the center is, but with a zero radius it is not a circle.
I dont know I need to sleep this off and maybe I'll just accept x≥0 as domain for geometrical area.

Answer 9

zero length exists on number line

Answer 10

length of AA is 0 on number line

Answer 11

circle wid radius 0 is a convoluted conic section, which exists as a point at the intersection of two cones