Logic

Dr.Peterson said:
Since it is always true that sin^2(x) + cos^2(x) = 1, you can always replace it with 1. Always! You need no additional information to make that permissible.

Why would you even imagine you couldn't??
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I have no idea why I imagine that I couldn't , but I frankly face that problem, I know there's identity sin^2(x) + cos^2(x) = 1 , but ! while solving like if I have another problem like
Sin(x)^2 + Cos(x)^2 = X^2+Y^2+Z^2 .. so here i STUCK although I know that there's
sin^2(x) + cos^2(x) = 1 but the question why I could assign that?! here what's exactly I'm facing while solving question ...

maybe because sin^2(x) + cos^2(x) = 1 it's not given explicitly like sin^2(x) + cos^2(x) = 1 ..... so I get mislead while it's given with other equation like Sin(x)^2 + Cos(x)^2 = X^2+Y^2+Z^2....how can I solve that problem of thinking ?!!
 
Ryan$ said:
I have no idea why I imagine that I couldn't , but I frankly face that problem, I know there's identity sin^2(x) + cos^2(x) = 1 , but ! while solving like if I have another problem like
Sin(x)^2 + Cos(x)^2 = X^2+Y^2+Z^2 .. so here i STUCK although I know that there's
sin^2(x) + cos^2(x) = 1 but the question why I could assign that?! here what's exactly I'm facing while solving question ...

maybe because sin^2(x) + cos^2(x) = 1 it's not given explicitly like sin^2(x) + cos^2(x) = 1 ..... so I get mislead while it's given with other equation like Sin(x)^2 + Cos(x)^2 = X^2+Y^2+Z^2....how can I solve that problem of thinking ?!!
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Again, you make up some problem to confuse yourself.

expression one = expression two.

All that means is that the two expressions represent the same numeric value.

[MATH]cos^2(x) + sin^2(x) = \text {some expression.}[/MATH]
But no matter what x is [MATH]cos^2(x) + sin^2(x) = 1.[/MATH]
So [MATH]cos^2(x) + sin^2(x)[/MATH] and 1 are just different names for the exact same numeric value.

And because you have stipulated that [MATH]cos^2(x) + sin^2(x) = \text {some expression.}[/MATH],

then some expression is just a third name for the exact same numeric value, namely 1.

The equal sign simply means "has the same numeric value."

You asked this exact same question using x, y, and z weeks ago.

Here is a BASIC rule of algebra: [MATH]x = y \text { and } y = z \implies x = z.[/MATH]
Learn it and move on.
 
thanks alot but for instance lets assume I have like this
np*(5+y)
and np is equal to ni^2/C
then I know that's np=ni^2/C BUT once I solve an equation like this np*(5+y) it rings in my head that
np = ni^2/C , but I don't assign it because I ask myself who said that I'm allowed to "assign" .. yea they are equal but who said that I could assign in the equation np*(5+y) ..

I hope I explained my problem, you know it rings in my head that np=ni^2/C .. but I'm not assigning it although it rings in my head ni^2/C .. idk what's that approach? am I facing that problem alone? or maybe my iq isn't ... ? but it rings for me that np=ni^2/C .. but not assigning that in my equation ..
 
Ryan$ said:
thanks alot but for instance lets assume I have like this
np*(5+y)
and np is equal to ni^2/C
then I know that's np=ni^2/C BUT once I solve an equation like this np*(5+y) it rings in my head that
np = ni^2/C , but I don't assign it because I ask myself who said that I'm allowed to "assign" .. yea they are equal but who said that I could assign in the equation np*(5+y) ..

I hope I explained my problem, you know it rings in my head that np=ni^2/C .. but I'm not assigning it although it rings in my head ni^2/C .. idk what's that approach? am I facing that problem alone? or maybe my iq isn't ... ? but it rings for me that np=ni^2/C .. but not assigning that in my equation ..
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Just stop making up these goofy examples. They frequently make no sense.

np * (5 + y) is an expression. It is NOT an equation. An algebraic expression has little meaning on its own.

"Ringing in your head" and "assigning" make no sense except perhaps in describing to yourself your own pschology. We are not psychiatrists. If two expressions have the same numeric value, it should be clear that it makes absolutely no numeric difference which you use. You can use whichever is more convenient for your purposes.
 
Here's a hypothetical question for you Ryan. Do these sentences mean the same thing?
1. I find mathematics difficult.
2. I find mathematics hard.

Yes they do, because we know that the word "difficult" and the word "hard" are synonyms, ie have the same meaning in this context. So we can interchange them because we know they mean the same thing. The meaning of the sentence doesn't change. We could say difficult = hard.

It's the same deal in maths. If we know that sin^2(x) + cos^2(x) = 1, which it ALWAYS does, then we can interchange them. Wherever we see sin^2(x) + cos^2(x) in an equation or an expression, we can replace it with 1.
 
You need to understand what equal means.
If klegjagkj= hjsaoaf then whenever you see klegjagkj you can replace it with hjsaoaf and whenever you see hjsaoaf you can replace it with klegjagkj.

Now in a given problem you are told for example that x+y = 9. So in this problem if you see x+y you can replace it with 9 and if you see 9 you can replace it with x+y.

Now x+y=9 is NOT an identity equation as it is NOT always true. However you know that 2+3=5. So if in your work you have 2+3 I bet you would replace it with 5. Now just like 2+3=5 we have sin^2(x) + cos^2(x) = 1 ALWAYS. So you can replace sin^2(x) + cos^2(x) =with 1 without any real thinking just as you would replace 2+3 with 5.

Just understand that just because you know very well that 2+3=5 and maybe don't really know why sin^2(x) + cos^2(x) = 1 they are still identities non-the-less.

So much is 7 + 4(sin^2(x) + cos^2(x))
 
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Hi guys! please I'm struggling that problem every day and I want to cut off that struggle totally.

lets assume I have equation like X^2+Y^2+Z^2=M^2 and didn't say anything about it, so it's in general.

afterwards we have conclude over specific case that case is satisfying the equation over specific parameter like Z=0 , then can I say that "specific case" is satisfying that equation: X^2+Y^2=M^2 ?! if so then why? I'm stuck in that struggle everyday, how we can assign specific parameter over specific case and then we say it's satisfying the general equation over specific parameter ! ?!
 
Please don't try to generalize your questions. Instead, give a specific problem that you are actually working on, so we can see the real conditions under which these questions arise. Ask your question about such a specific problem, so that we can tell exactly what reason there is for each claim.

Until you cooperate in this way, you will not get satisfactory answers.
 
Yes, if you have a "general equation" of the form \(\displaystyle X^2+ Y^2+ Z^2= M^2\), and Z=0, then, because Z=0, you can replace "Z" by "0" to get \(\displaystyle X^2+ Y^2+ 0^2= M^2\) which is \(\displaystyle X^2+ Y^2= M^2\). I'm not sure what you mean by "satisfying the general equation over specific parameter". Setting Z=0 changes the "general" equation to a less general equation. (I wouldn't say "specific" because X and Y can still be any value.)
 
Hi guys, I just would like to verify:
if given A related to B , then why it's right to say that B related to A?! I really get confused .. who said that related is bi-directional ? I mean
A -->B
then it's right
B--->A



?! what does that math means when say "Related" ?
 
Please quote exactly your source, and also quote the definition given for "related". That will suggest "who said".

The term that is usually precisely defined is not "related" but "relation". But if there is a relation from A to B, then we can define a relation (the inverse) from B to A, so we can say that each is "related" to the other (technically by different relations).
 
Dr.Peterson said:
Please quote exactly your source, and also quote the definition given for "related". That will suggest "who said".

The term that is usually precisely defined is not "related" but "relation". But if there is a relation from A to B, then we can define a relation (the inverse) from B to A, so we can say that each is "related" to the other (technically by different relations).
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Hi I'm asking in general !
I need to understand the meaning of "relation" ! if I told you A related to B , what you understand from this?! here's my point..
 
If your textbook has an exercise in which it is stated that "A is related to B" then I would expect your text book to have a definition of "relation"! The standard mathematical definition of "relation from set A to set B" is "a subset of AxB" or, equivalently, a set of ordered pair, (x, y), such that x is in A and y is in B. Certainly if "A is related to B" so that there exist such a set of pairs, (x, y), then there exist a set {(y, x)} so B is related to A. However, those are two different relations.
 
Let me demonstrate what I'm asking of you. I will quote a source that uses the phrase "a is related to b", including its definition. You'll note that my example is not quite the same as what we have been talking about, because my example has a and b in lower case (representing elements of sets), not in upper case (representing sets themselves). [I couldn't find an example where A and B are sets.] This is why we ask for exact quotes of what you are asking about, so we can be sure what you are referring to. This may or may not be what you are asking about!

Here is the source:


Here is their definition:

In mathematics, a binary relation over two sets A and B is a set of ordered pairs (a, b) consisting of elements a of A and elements b of B. That is, it is a subset of the Cartesian product A × B. It encodes the information of relation: an element a is related to an element b if and only if the pair (a, b) belongs to the set.​

Here we are using the phrase "is related to" in the context of a specific relation (that is, a specific set of ordered pairs, which "relates" certain elements of set A to certain elements of set B). If there were more than one relation being discussed, we would have to say more specifically, "a is related to b by relation R", or we would write specifically "a R b" to express that.

In this usage, it is not true that if a is related to b, then b is related to a, except in very special cases (symmetric relations). Again, I can't tell from what you asked whether your source says that this is always true, or sometimes true; whether you are asking how it can ever be true, or whether it is always true. We need to see your exact context in order to know what you are asking.

Here is an example from my source:

An example is the "divides" relation over the set of prime numbers P and the set of integers Z, in which each prime p is related to each integer z that is a multiple of p, but not to an integer that is not a multiple of p. In this relation, for instance, the prime 2 is related to numbers such as −4, 0, 6, 10, but not 1 or 9, and the prime 3 is related to 0, 6, and 9, but not 4 or 13.​

Here 2 is related to 6, but we could not say that 6 is related to 2 [by this relation], because 6 is not in the set of prime numbers. It wouldn't even make sense to ask whether it is! On the other hand, we can define the inverse relation "is divisible by", and then 6 is related to 2 by this relation.

Now it's your turn: Show us what you read that led to this question, so we have something definite to talk about. If you can't learn to do this, then people on this site are only going to continue complaining about your lack of cooperation.
 
Hi guys!
I'm a lil confused on something which it could be easy to others!
if I have something that's satisfying specific formula, like the current = voltage/R in physics ..
I need to calculate specific current which means I1 so it should be I1=voltage1/R1 .. but the teacher is telling like this:
I1=voltage/R =voltage1/R1

what's confusing me writing I1=voltage/R and not voltage1/R1 ..is a wrong writing ,,yeah? because I1 must be I1=voltage1/R1 AND NOT I1=voltage/R =voltage1/R1
am I right? what's confusing me the term of writing i1=voltage/R !! it must I1=voltage1/R1 without writing i1=voltage/R
I mean the term voltage/R is right in general ! so we shouldn't write it over specific case like i1 !!
any help please?!
 
if something is satisfied in general like I=U/R
and I want in specific like I1 !
so I should write I1=U1/R1 and not writing I1=U/R=U1/R1 ..because U/R is right in general and not right in specific ... right?!
 
I agree that the extra step of I1 = U/R is not needed. But if your teacher wants you to follow this rule, just do it.
 
Ryan$ said:
if I have something that's satisfying specific formula, like the current = voltage/R in physics ..
I need to calculate specific current which means I1 so it should be I1=voltage1/R1 .. but the teacher is telling like this:
I1=voltage/R =voltage1/R1

what's confusing me writing I1=voltage/R and not voltage1/R1 ..is a wrong writing ,,yeah? because I1 must be I1=voltage1/R1 AND NOT I1=voltage/R =voltage1/R1
am I right? what's confusing me the term of writing i1=voltage/R !! it must I1=voltage1/R1 without writing i1=voltage/R
I mean the term voltage/R is right in general ! so we shouldn't write it over specific case like i1 !!
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You appear to be expecting that if variables like I, U, and R are used in a general formula, then it is required that the same variables with the same subscript (I1, U1, R1) must be used in any specific application. That just is not true.

If R is given as a constant resistance, for instance, you don't need to subscript it. Or in a parallel circuit, each resistance may have its own current (I1, I2), but they all have the same voltage drop (R, no subscript needed). Specific instances do not always have subscripts. Sometimes we use the same variable name given in the formula, to represent a specific value, because there is no reason to give it a new name.

I would expect that in writing "I1 = U/R = U1/R1", a teacher may just be first reminding you of the formula, and then applying it. That shouldn't be too confusing.

But, as with many of your questions, we can't really know what you are asking about, and how much of your complaint is valid, without seeing the specific context. Please show us a link or picture of what this person is actually saying, rather than merely describing it in general.
 
Dr.Peterson said:
You appear to be expecting that if variables like I, U, and R are used in a general formula, then it is required that the same variables with the same subscript (I1, U1, R1) must be used in any specific application. That just is not true.

If R is given as a constant resistance, for instance, you don't need to subscript it. Or in a parallel circuit, each resistance may have its own current (I1, I2), but they all have the same voltage drop (R, no subscript needed). Specific instances do not always have subscripts. Sometimes we use the same variable name given in the formula, to represent a specific value, because there is no reason to give it a new name.

I would expect that in writing "I1 = U/R = U1/R1", a teacher may just be first reminding you of the formula, and then applying it. That shouldn't be too confusing.

But, as with many of your questions, we can't really know what you are asking about, and how much of your complaint is valid, without seeing the specific context. Please show us a link or picture of what this person is actually saying, rather than merely describing it in general.
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THANKS ALOT VERY INFORMATIVE!
and yeah the teacher was reminding for of the formula, but is it allowed to write that?! that's my confusion ! I mean is it allowed to write I1=U/R ? and then =U1/R1 ??
 
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