# point in math and continuous function: Is there more than smaller to the point?

##### Junior Member
Wow convinced me about point in away that I cant say anything
Another thing then why we assume that value is corresponded to a point and not for example a value corresponded to semi-point? I mean maybe value occupy two points at one time? Who claims that value number is corresponded to one point at a time?

#### Dr.Peterson

##### Elite Member
Math is invented so that it represents the concepts we are trying to represent, as simply as possible. Assuming that each number corresponds to one location on a number line agrees with what we expect from generalizations of the real world, and makes calculations easy, so we go with that (and have for a very long time).

Now, perhaps you could invent a new kind of geometry in which there was such a thing as a "semi-point" and there were two numbers in the same place on a number line; but you probably couldn't get anyone to try using it, because it would be too cumbersome with no benefits. That's not to say it would necessarily be "wrong".

Mathematicians do invent new mathematical objects or systems, just to see what will happen! And sometimes the results turn out to be useful, even if they weren't trying to make something that corresponds to the real world. But if what they invent is not either useful or interesting, their paper will just gather dust, even if it's perfectly valid, because there will be no motivation for anyone to pursue it further.