Logic

Hi guys, sorry about that but maybe I magnificent the subject and I understand it wrongly so I need to understand it well.

what does it mean in math that X dependence to y? and if not dependence to y, what does that mean mathematics?!
to be more clear, how dependency and not dependency represented in aspects of math? and if not dependent then not dependent and it's concrete..... like black or white yeah? no more choices ..
 
tkhunny said:
Possibly an arbitrary choice. y = f(x).
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didn't understand that. but I can also write y=f(x)=constant then what? is y depend on x or not? the syntax y=f(x) still telling you that y is related to x .. ! but might be f(x)=const as?!
 
If y= f(x) and f(x) is defined to be a constant, then the value of f(x) is the same no matter what x is. The value of y is constant, and so the value of y does not depend on x. y is not dependent on x.
 
[MATH]y = |x|.[/MATH]
GIVEN THAT, y is dependent on x because you can determine what value y has if you know what value x has, but you cannot determine what value x has if you know only what value y has.

In terms of function notation, [MATH]y = f(x)[/MATH],

we say that y is the dependent variable because you cannot know what the value of the function is until you know what value x has.
 
Ryan$ said:
Hi guys, sorry about that but maybe I magnificent the subject and I understand it wrongly so I need to understand it well.

what does it mean in math that X dependence to y? and if not dependence to y, what does that mean mathematics?!
to be more clear, how dependency and not dependency represented in aspects of math? and if not dependent then not dependent and it's concrete..... like black or white yeah? no more choices ..
Click to expand...
First, we have to figure out what the proper English for your question would be; when you ask about what is largely a language issue, language errors tend to get in the way. Here is my attempt to rewrite this as it might really be intended (that is, this is a guess):

What does it mean in math that x depends on y? and if x does not not depend on y, what does that mean mathematically?!​
To be more clear, how are dependence and non-dependence represented in aspects of math? And are these the only possibilities, so that a variable is either dependent or not dependent, and it's concrete..... like black or white? No other choices?​

(I'm making no attempt to figure out what you meant by using "magnificent" as a verb. I presume that was just a slip.)

When we say that (within a particular problem) x depends on y, we are saying that we are taking y to be the independent variable, which is considered to be assigned a value without reference to the other, and x to be the dependent variable, meaning nothing more than that x is being thought of as a function of y, that is x = f(y) for some function f.

There are other possibilities; we could have taken x and y to be both independent, and something else to depend on them, or each might depend on some other variable.

Also, this says nothing inherent about either variable; it reflects only the relationship we are thinking about. In particular, would could often think of either variable as dependent on the other; for example, in a graph, we could choose to make height a function of arm length, or arm length a function of height. (In reality, neither is determined by the other -- both are determined by other factors.)

Ryan$ said:
but I can also write y=f(x)=constant then what? is y depend on x or not? the syntax y=f(x) still telling you that y is related to x .. ! but might be f(x)=const as?!
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If the function happens to be a constant, then all that says is that y is itself constant. We are still calling y the dependent variable, but that doesn't mean much, as the dependence is trivial. We can at the same time say that y is independent of x, which is not the same as being the independent variable. Again, dependence says nothing about the variable, or even about any real relationship between them, but only about how we are choosing to look at them.

As an example, consider the famous experiment in which objects are dropped from a fixed height to see which hit the ground fastest. We are trying to determine the dependence of fall time on mass; if it turns out that the time is always the same (independent of mass), then we are finding that this is a constant function. In our calculations, we are treating mass as the independent variable, and determining that the dependent variable is in fact constant. We are then finding that in reality time is independent of mass.

Ultimately, I think you need to ask these questions of someone who speaks your language, quoting actual problems in the original language, and asking how that language is used. Your language may have different ways to express these ideas, so what we say about English may be irrelevant to you. Optionally, you could quote the original to us in that language, in such a form that we can use Google or other means to translate it ourselves, and if we want to take the time, try to answer you. To do more is probably a waste of your time and ours.
 
Dr.Peterson said:
… I think you need to ask these questions of someone who speaks your language …
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This suggestion has already been made (more than once). We asked also whether he could find someone who speaks English.

… you could quote the original … we can use Google or other means to translate it ourselves …
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We've already tried this suggestion, too. Ryan doesn't seem interested in helping us.

To me, Ryan seems like another harpazo -- someone who never learned basic math in school but for some reason now wants to play around with math subjects beyond middle school, jumping from topic to topic while not absorbing so much as perusing. In other words, not a serious student.

?
 
That's why I usually ignore his threads; I figure nothing I say will help. In this case, the question seemed potentially valid.

It would be nice to know something about his actual situation, though. I have several competing theories.
 
Hi ! once again I'm too much sorry for posting here, but you guys help me alot as I learn solo,
if I have arrived to conclusion when I solve a problem like " IN GENERAL FOR ALL CASES my SOLUTION MUST WORK TO THEM ALL" , so are we concluding from this if I have specific case from the all "general cases" must work accordingly to my solution which I solved in general? I means if I solve a problem in general, so must any concrete cases work accordingly to my general solution that I solved?
I'm confused about the meaning of "general" , and who said that "general solution to my problem" means all cases must work accordingly to my solution? maybe there's a specific case not working accordingly to my general solution .. so my general solution wouldn't be called "general solution" to my problem?!

I try to analogy that to my logic, A (general sol.) --->B(all specific cases) which means
"general solution" ----> "all cases must be satisfied", but who said that
"all cases must be satisfied --------> general solution"

in logic if A ---->B **(like my situation)*** , then it's not necessary that B--->A it's not bi-directional ..
 
Strictly speaking, yes, any "general solution" should include all "specific solution". However, it does sometimes happen (especially in solving non-linear differential equations) that we can get a formula that gives all solutions except a few special ones. It is an 'abuse of notation' to call that a "general solution" but it is some times done.
 
You have been told repeatedly to provide specific problems, not analogies to what you think may be some general class of problems. Frequently your questions seem to reflect confusion about the English language.

Yes, strictly speaking, a general solution to a class of problems provides a template for solving any problem in that class.

For example,

[MATH]\text {Given } a,\ b,\ \text { and } c \text { are all real numbers}.\ a \ne 0, \text { and } ax^2 + bx + c = 0, \text { then }[/MATH]
[MATH]\text {there is no real solution if } b^2 - 4ac < 0;[/MATH]
[MATH]x = -\ \dfrac{b}{2a} \text { if } b^2 - 4ac = 0, \text { and}[/MATH]
[MATH]x = \dfrac{-\ b + \sqrt{b^2 - 4ac}}{2a} \text { or } x = \dfrac{-\ b - \sqrt{b^2 - 4ac}}{2a} \text { if } b^2 - 4ac > 0.[/MATH]
That is a general rule that will work for any problem that exactly fits the specifications given. It will not work if, for example, a equals zero.
 
Hi guys, I'm sorry to post like this post here but I find it hard to accept what's I'm going to say !
if A=B , is it the same to say B=A? if it's, then why? what's confusing me A=B isn't in writings the same B=A so how we determined that A=B is the same as B=A!!!!!
I know it's equal, but who said we just care on equal? maybe also on the order of writing the elements of two sides of equation .. who said not?!
 
In any Math system I have studied we have to have that A = B implies B = A.

For example: If we know that x = 2 then we also know that 2 = x. The order is unimportant.

-Dan
 
Ryan$ said:
I find it hard to accept what's I'm going to say !
if A=B , is it the same to say B=A? if it's, then why? what's confusing me A=B isn't in writings the same B=A so how we determined that A=B is the same as B=A!!!!!
Click to expand...
You know that Samuel Clemens is Mark Twain.
Would you be bothered by someone saying Mark Twain is Samuel Clemens?
 
Ryan$ said:
if A=B , is it the same to say B=A? if it's, then why? what's confusing me A=B isn't in writings the same B=A so how we determined that A=B is the same as B=A!!!!!
I know it's equal, but who said we just care on equal? maybe also on the order of writing the elements of two sides of equation .. who said not?!
Click to expand...

Since another question hints that you know something about computer programming, it may be worth pointing out that "=" can be used in different ways. Sometimes order doesn't matter, sometimes it does.

"Who says?" This is just an implicit agreement among users of the notation, in a particular context -- like all language! If you choose to be part of a community, and communicate with them, you use the words and symbols they use, in the way they use them.

In math, "=" by itself always means merely "is equal to". When we say that A = B, it means that quantities A and B are equal -- both quantities play the same role; it doesn't matter which order you put them. You can think of it as bidirectional, or symmetrical. (It can also be used in a definition, as in "let n = 3", which is not symmetrical; but even there, "=" just means these two quantities are equal; it is the sentence in which it is found that changes it from a mere statement of equality to a definition.)

This is what all mathematicians accept as the meaning. And this is what the symbol has meant since it was first invented, as described here.

But some programming languages use "=" in a different way, meaning "is assigned", similar to the usage in definitions. There, writing A = B means "put the current value of variable B into variable A". This is one-directional; it actually tells the computer to do something to variable A, and not to B. For example, in programming you can say "x = x + 1", which in math would be nonsense, but in a program changes the value of x by adding 1 to it.

Similarly, in English, the word "is" can be used in different ways. Taking pka's example, "Samuel Clemens is Mark Twain" means that they are two names for the same person; but "Samuel Clemens is an author" describes one aspect of Clemens, and identifies only one of many people who are authors -- it doesn't equate all that Samuel Clemens is with all authors. Or, returning to math, we can say "a square is a rectangle" but "a rectangle is a square" means something very different; this usage is asymmetrical.

But many students think of "=" in math as if it meant "has the answer", as in "2 + 3 = 5" meaning "if you add 2 + 3, the answer you get is 5". That is a misunderstanding; it really means merely that 2 + 3 and 5 are two "names" for the same quantity. When you move from arithmetic into algebra, you have to leave that earlier way of thinking behind.
 
Hi guys ! I hope this thread wouldn't be closed because I really struggle that and I need to understand and LEARN!

if I have any equations doesn't matter what it's , for instance f(x) = x^2+6 , I've a problem that I deeply know if I want to move forward in the solution then I must assign into the equation , I mean, I have a case in my problem/question which I must assign into the equation x0 (*specific case* but it's satisfy the equation) , then my question can I assign f(x0)=(x0)^2 + 6 and continue with my solution? what I mean by that I have the equation in general "f(x)=x^2+6 " , in whatever way in my question I arrived to conclusion that x0 in my question must satisfy the equation, then can I assign it into the equation? what's confused me x0 is a specific case that must satisfy the equation .. but the equation is general case .. so how do we assign speicfic x0 into the equation which it's general?





another question, the teacher in the video said if we have X(Y+Z) and we already know that Y is regardless to Z then X(Y+Z) is approximated to X*Z , why it's right? I mean why it's right to disregard Y which it's inside the parentheses .. if it was Y+Z explicitly without any parentheses then I accept the approximation .... what's confusing me why it's allowed to disregard what's inside the parentheses without worrying what's going out of the parentheses !
 
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Firstly you need to now the difference between:
1. an expression like x2+6 ….. possibly can be factorised, expanded or simplified (not in this case)
2. an equation like x2+6 =10 …… can be solved (ie what value of x makes it true)
3. a function f(x) = x2 + 6 OR y = x2+6 …. shows a relationship and can be graphed
 
In general we have the definition \(\displaystyle f(x) = x^2 + 6\) so if we have any specific value of x in mind, such as \(\displaystyle x_0\), then \(\displaystyle f(x_0 ) = (x_0 )^2 + 6\), as you say. Any value of \(\displaystyle x_0\) will do.

\(\displaystyle f(1) = 1^2 + 6 = 1 + 6 = 7\)
\(\displaystyle f(-3) = (-3)^2 + 6 = 15\)
\(\displaystyle f(85786) = (85786)^2 + 6 = 85786^2 + 6 = 7359237802\)
\(\displaystyle f(0.34699) = (0.34699)^2 + 6 = 6.1204020601\)

etc.

-Dan
 
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