# Axis Y and X

##### Full Member
Hold on you're telling me too many things like I'm skilled in math ... one by one lemme understand

what do you mean by standard ? if something is standard then allowed in math to call it whatever ?!

what's confusing me why we are allowed to call them whatever we want? who said it's allowed in math ..?

#### Dr.Peterson

##### Elite Member
You can call a pair of axes anything you want. We customarily call them x and y when there is no reason to call them something else; but graphing is a tool you can use as you wish, not a tyrant that restricts what you can do. (That's true of all of math, actually.)

Often, the horizontal axis is used to represent an independent variable (for example, time), and the vertical axis is used to represent a dependent variable (say, temperature). Have you never seen graphs representing anything like that?

In abstract problems, we tend to call the independent variable x and the dependent variable y; but in applied problems, we use the natural names appropriate to the problem.

The real question is, why would you think this is not allowed? What would be the benefit of such a restriction?

When a teacher tells you to do something, go along with it, rather than acting like you know better than the teacher! Perhaps your experience is less than his.

#### JeffM

##### Elite Member
The letters that we use to stand for variables are ARBITRARY, and what a given letter represents varies from problem to problem. I believe that you have been told this before. This is one of the reasons that you should define your terms at the beginning of every problem.

It is a conventional to use x for the independent variable, and y as the dependent variable. And it is conventional to use the vertical axis for the dependent variable, and the horizontal axis for the independent variable. But no one is obligated to abide by these conventions.

#### Otis

##### Senior Member
… lemme …
Why are you allowed to use that word? Who said it's allowed?
$\;$

##### Full Member
The real question is, why would you think this is not allowed? What would be the benefit of such a restriction?
to be more frankly with you, it's struggling me every time I want to think, I go along "allowed" or not "allowed" .. "who said that"? and like this abnormal things.
I don't know why am I going along these movements, but I should do something to cut off those things.

Maybe if you've an approach or something to let me follow while thinking ... it would be much appreciated. exactly if you've something to instruct me and convince me that saying "who said that" ..etc while thinking is a wrong approach and mislead my thinking to solve the question ..

I appreciate your effort to help me, and I hope you help me to how should I think ..I mean to cut off those "who said that" , "it's allowed" ... while thinking ..

thanks

#### Otis

##### Senior Member
Otis said:
Who said [lemme is] allowed?
… I don't know ! … I face that struggle [with everything] …
Ryan, my point is this: You don't need to be concerned about 'lemme' because it's common English slang. People already accept that it means 'let me' so nobody needs to struggle over its use or ask whether it's allowed. (It probably would not be allowed in a formal English writing assignment, but we don't worry about such stuff here.) Almost nobody cares where the word lemme originated or who said it first, so those questions don't need to be asked.

In other words, 'lemme' means 'let me' is given information. Once we've been told (i.e., learn it), we use it. We don't worry about it. We accept it as true because we hear it regularly and it works. I'm sure you agree; after all, you used the word lemme without any concerns. You ought to do the same with givens in math.

Here is how most math students learn given information. They participate in a structured course of study (eg: they go to class). They study many pieces of given information (eg: definitions, relationships, patterns, methods). Next, they practice remembering and recognizing the information they've been given. (Successful students practice A LOT.) They don't question given facts. They don't worry about original sources. They simply accept lessons as true because the instruction says so.

Speaking for myself only, I've become disinterested in trying to help you because I see no goal. Therefore, I'm going to let other members respond to your posts from now on. I wish you good luck with whatever it is that you're trying to accomplish. Cheers
$\;$

#### Jomo

##### Elite Member
A graph describes one value in terms of another value. For example, how much someone eats vs their weight. How far someone travels vs their speed, How much money you earn per week vs how many hours you work per week.

And of course you place the graph on the x-y plane

##### Full Member
It's your triangle and your coordinate system. You can decide where to put the corners.
So there's no specific solution? I mean who would solve the question will assign its own coordinate system and then the solution would be different from whom coordinate is different no?

#### MarkFL

##### Super Moderator
Staff member
Solution to what? You haven't stated a problem.

#### lev888

##### Full Member
So there's no specific solution? I mean who would solve the question will assign its own coordinate system and then the solution would be different from whom coordinate is different no?
What solution? For the millionth time - in order to talk about a solution we need an exact problem statement. A question like "Can I decide which corner of a triangle I can put on an axis?" is not something that has a solution.

#### Dr.Peterson

##### Elite Member
So there's no specific solution? I mean who would solve the question will assign its own coordinate system and then the solution would be different from whom coordinate is different no?
If you have some problem to solve, and as part of your work you choose to introduce a coordinate system, you can place it any way you find convenient. If the method and the implementation are valid, then the solution you get will not depend on the choices you make; anyone else will get the same answer you get. There is not one specific solution method.

There is far more freedom in mathematics than you are aware of! It is not a set of restrictive rules you must follow blindly and fearfully; it is a set of tools that you can use at will, without having to constantly worry whether you are doing "the right thing". Enjoy that freedom!

#### Ryan\$

##### Full Member
If you have some problem to solve, and as part of your work you choose to introduce a coordinate system, you can place it any way you find convenient. If the method and the implementation are valid, then the solution you get will not depend on the choices you make; anyone else will get the same answer you get. There is not one specific solution method.

There is far more freedom in mathematics than you are aware of! It is not a set of restrictive rules you must follow blindly and fearfully; it is a set of tools that you can use at will, without having to constantly worry whether you are doing "the right thing". Enjoy that freedom!
So, my question is how to know it's valid or not? I mean yeah once I solve a question I'm not finding there's something not allowing me to not using it, but still in my head , who said it's valid ?!

#### Dr.Peterson

##### Elite Member
So, my question is how to know it's valid or not? I mean yeah once I solve a question I'm not finding there's something not allowing me to not using it, but still in my head , who said it's valid ?!
Please stop asking "Who said?" Just learn the math, and do what you are taught to do. That will be valid. (That is, if your teacher said to do something, then you can do it! Ultimately, most things are based on theorems that can be proved, so you can trust them.)

There is absolutely no reason you couldn't choose any point in the plane as your origin, and any direction as your x-axis. This is an arbitrary choice. If you think otherwise, do you have a reason?

#### lev888

##### Full Member
Let's say your house number is 20, your friend lives in 24. How many houses are between you and your friend? One - #22. Let's put the "origin" at the other end of the street. You are now in 15 and your friend is in 11. How many houses are between you and your friend? Still one. Now matter where you start house numbers the answer will remain the same.

#### JeffM

##### Elite Member
Actually, I am going to take my life in my hands and disagree with Dr. Peterson.

The math that you are being taught is based on a set of axioms. Axioms are things that you accept as true on faith (or a "willing suspension of disbelief"), but all the rest of a system of mathematics is proved logically from those axioms. There is nothing that says you must accept those axioms. In that case, you are free to build a completely new mathematics developed logically from a different set of axioms.

The mathematics that you are being taught is based on axioms that are very extensively validated by experience in the real world. For example, one of its axioms is

$$\displaystyle \exists \text { no pair of elements of the set such that } a * b \ne b * a.$$

Experiment with a few hundred pairs of real numbers to see whether this axiom is ever inconsistent with experience. So we use the system based on the axiom above for real numbers.

But it is perfectly possible to develop a mathematical system based on an alternative axiom, namely

$$\displaystyle \exists \text { pairs of elements of the set such that } a * b \ne b * a.$$

Although the set involved is not that of real numbers, that axiom can be demonstrated as consistent with experience of sets involving some kinds of thing (but not real numbers).

So the mathematics that you are currently studying is based on axioms, which you are to assume are true, and theorems, which have been proved to be true if the axioms are true. There is no need to ask who says so. You are assuming that they are so. (And no one has found a real number for which they are not so.)

You are free to create a different mathematics (though it is likely to be completely useless in the world of experience). And to the extent that you accept the axioms and theorems of the real number system, you are free to create any assumptions that do not implicitly contradict the axioms and theorems of the real number system.

In the centigrade system of measuring temperature, 0 is the highest ambient temperature at which pure water freezes. In the Fahrenheit and Kelvin systems of measuring temperature, 0 is not the highest ambient temperature at which pure water freezes. In the different systems zero has a different physical meaning. Where you set the origin of a coordinate system is arbitrary.

Now Dr. Peterson gave you very good advice. When your teachers and texts say something is always true, just accept it and learn the mathematics that results from those statements. You are not going to learn anything of practical or theoretical use if you keep wondering whether it is true that 7*3 = 3*7. There may be alternative mathematics, but the mathematics that you are being taught, the mathematics of real numbers, is of major practical importance because it is what is consistent with quantities counted or measured in macroscopic, physical reality. 7 sets of 3 balls each add up to a total of 21 balls in all and so do 3 sets of 7 balls each.

You are wasting incredible mental energy asking why certain things are true when the process is about why some things are true if certain other things are true. It is simply stupid to ask why the certain other things are true. They are assumed to be universally true because no contrary example has ever been found.

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