# point in math

##### Full Member
A question for you: Do you accept that 0.9999..... = 1?

frankly NO , that's why I'm getting confused .. why would you accept that 0.999999 =1? so in other words we are not solving the problem "exactly" we are approximating it !

##### Full Member
Actually what I imagine a point as something that have quantity(value) that's why I'm finding it hard to solve problems in math, and why I imagine that is, because I'm not convinced that point is something not found or actually "empty"

#### Otis

##### Senior Member
so I can say that [a] "point" can be visualized in [the] mind as something [that] isn't found [in the real world] …
Yes. We use the idea of points to help us visualize numerical objects.

… and [in] math [a] point is about "nullity" [or] nothing and doesn't affect my solutions?
Well, the word nullity infers no usefulness. Points are very useful, in mathematics. We use them as models, to represent numerical values.

The Real number line is composed of an infinite collection of points. Each point on the number line represents a specific Real number. Likewise, for every Real number, there is a point on the line.

When we measure a specific distance on the Real number line, we subtract the smaller number from the larger number, yes? For example, what is the distance from -4 to positive 4?

We subtract the smaller number from the larger number:

4 - (-4) = 8

The number 4 is represented by the point which is exactly four units to the right of zero. The number -4 is represented by the point which is exactly four units to the left of zero. These two points are the 'endpoints' of the interval.

In the real world, if we use a measuring device (like a ruler), we can't measure exactly 8 units, but what we see is close enough. That is, if we were to use a very precise measuring device, the measurement might show 8.0000000000000000000000000000000000203956…

In the real world, the average person won't care about those non-zero digits (starting around the 40th decimal place). Whether or not a mathematician cares about them, the mathematician understands they do exist.

Maybe you are perplexed because you're not yet thinking about infinity. Did you think about my earlier question? What is the smallest positive number? :cool:

Last edited:

#### Otis

##### Senior Member
Actually [I] imagine a point as something that [has] quantity (value) that's why I'm finding it hard to solve problems in math, …
A point represents a value. It is only a model (i.e., part of a system for organizing and visualizing relationships between numbers).

… I'm not convinced that point is something not found or actually "empty"
Fair enough. If you think a point is something that you can find in the real world, please give me an example.

A point represents a number, and that number has value. If you want to say that some point has value 4, that's okay, but saying it doesn't give the point mass (in any sense).

When you say that a point cannot be "empty", are you thinking about width? A point has no width. You cannot measure the width of a point. You cannot assign any value to a point, other than the specific number (eg: location) it represents.

Points are dimensionless.

If you think that a point has width (or some value different from the Real number it models), please give me a specific example.

Also, tell me in your own words what 'infinity' means to you. Cheers

#### Harry_the_cat

##### Senior Member
frankly NO , that's why I'm getting confused .. why would you accept that 0.999999 =1? so in other words we are not solving the problem "exactly" we are approximating it !
NO! 0.999999 does NOT equal 1. I did not say that.
What I said was 0.9999... = 1 , the … indicating a recurring decimal.

##### Full 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.

##### Full Member
Hi guys, I know that I already opened a thread about that subject but still struggling and by you I really boost myself.

when I imagine point, then I imagine a black box which if I split one of its points then its place will be white so it has dimension .. and that's wrong analogy .. can anyone help me how should I imagine point?! thanks alot

#### pka

##### Elite Member
when I imagine point, then I imagine a black box which if I split one of its points then its place will be white so it has dimension .. and that's wrong analogy .. can anyone help me how should I imagine point?!
In mathematics it is impossible to imagine a a point. Point is an undefined term. A point is something that just is.
In a famous example of a finite geometry bee hives are points.

#### Ryan\$

##### Full Member
Hi guys, I really want to verify about something it might be silly but I face it every time, and I want to verify if I just alone facing it or actually it's likely to others.
for example once I face something like subtraction such as : 4-5 then in my mind I imagine it like I have something continuous like this ----------------------------------------------- which its length is 5 and if I want to subtract 4 then I just remove 4 units from that line, what's confusing me that the mutual area or "point" is found between the removed area (the empty) and the reminder area .. exactly what I mean ----------------------------------- ------ , the right line is the subtracted area, and once I removed the left line (which it's like 4 because we are doing 5-4) then the point between the line removed and the left line is mutual between two lines(left and right) so doesn't it matter and change the quantity of 5-4 ?! I mean I claim that it would be matter because there's one point left from the ( "removed line" = 4 ) on the reminder amount of 5-4 ... and it's found because it's mutual between two lines so if I removed it from the left line , it would be still on the right line, doesn't that matter?!