Question

prove the theorem: The distance from a point to itself is zero. (is there an axiom i could use? I need explaination on how does this forms a line if any )

Answer 1

Line Integral from a number to itself = 0, something along those lines maybe

Answer 2

Use the length of a line formula for a quick proof.

Answer 3

delta x, or your change in x is found by xfinal -x initial. So let's say your # is 7. 7-7=0

Answer 4

there answers are not what i was looking for and i edited the question too. there can't be assumptions made without proving it first. i think it needs to form a line first but how can that be when there is only one point. maybe i'm overthinking it

Answer 5

Actually there is an axiom you can use. Distance usually implies the space you are working within is a metric space with a distance function. One of the axioms of the metric (distance function) in a metric space is that d(x, y) = 0 if and only if x = y

http://en.wikipedia.org/wiki/Metric_space#Definition

Answer 6

The problem is your question is too vague. What does distance even mean? I assume the types of spaces you are thinking of are euclidean spaces of various dimensions. But there are many many types of spaces in mathematics. In some spaces there isn't even a notion of distance. In fact it may not even be possible to define one. These are known as non-metrizable spaces.

Answer 7

yeah, thanks for your input.