Anyone who is really passionate about maths?

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Wow you're good!
Well you are all good, too good. What made me happy about NewDawns explanation is that it was explained in a way I understood
Thank you!

I'm a student in pure mathematics, and a high school/first year university math tutor, if you have something you're particularly stumped on you can message me.
I can't guarantee I'll get back to you right away but I know of a lot of online resources and I'm told I explain things very well/simply.

Thank you! I definitely will!

Okay. I can't resist this question anymore. Yes. I love mathematics, and am very passionate about it! I'm almost a mathaholic except for one thing: I suck at math. It is true that I have been re-teaching myself math for the past 3 years now by myself, and have only gotten up to just barely leaving the pre-calculus level, but man, when I get stuck on a problem, woe to anyone that is near me. I almost drive them crazy talking about it or thinking about it! I will not give up until I have solved it (or the last resort - look up the answer to learn how it was solved). I struggle more than most, but it fascinates me - to see new possible ways of observing things, and upon more advanced math, to see possible "universes"; it blows me away! Ladies, please don't run away; I have learned to keep this passion to myself, as most hate math, and will not talk about it unless you want me to. But I must confess my love here. It is not a total loss; I love music equally. I just won't play Stairway to heaven. (Wayne's World) lol

That is hot!
Why would anyone run away? I have always been attracted to math nerds and I'm sure I can't be the only one!
Of course it is super hot if you are good at it too but persistence and passion is super hot as well!
Sounds like you're slightly less hopeless than me Maybe you could explain the difference between a function and an equation to me?
I welcome anyone to do so!

[This is the "middle-school" definition. The formal mathematical definition is more complicated.]

A function is a construct that accepts numbers and maps each number onto another number. For example, the notation
"f(x)=x²"
defines the function named "f" by specifying that any number "x" is mapped onto the result of "x²". In this case, we get:
f(0)=0²=0, f(2)=2²=4, f(–1)=(–1)²=1, f(1.5)=1.5²=2.25, etc.

An equation is a very general construct to specify that two things are equal. More specifically, it states problem to be solved. For example, "find the number whose square is 2.56" is noted as:
"x²=2.56"
In general, an equation can have one, many or even zero solutions. In this case, if we permit "x" to be any real number, the equation has two solutions, namely "x=1.6" and "x=–1.6". The equation
"x²=0"
has the unique solution "x=0", and the equation
"x²=–1"
has no solution at all (unless we permit complex numbers, but that's a different story).

Functions may appear in equations. For example, we can first define "f" by
"f(x)=x²"
and then state the equation
"f(x)=0.25",
in which case the possible solutions are "x=0.5" and "x=–0.5".
This notation is a bit confusing because "f(x)=x²" contains an "=" sign and therefore looks like an equation, too. In fact, it is an equation because it specifies that "f(x)" equals "x²" for all "x", but there's nothing to solve; whereas "f(x)=0.25" should be read as: "find all choices of 'x' for which 'f(x)=0.25' is valid", making use of the previously defined property "f(x)=x²".
If you want to define a function and make sure that the reader doesn't think of the definition as an equation to solve, then write
"f(x):=x²"
or
"f(x)=x for all x"
or even
"The function 'f' is defined by: f(x)=x"

Cool! I'll do my best. Please bear with me, as this is very lengthy.

I will try to make this simple, as I honestly don't know what you know or don't know. If you know all of this stuff...then go down to the last paragraph; if not, then read from here:

An equation means that something on the left side is equal to something on the right side; for example, x = 2. That mysterious variable on the left (Let's call him Mr. X) is hiding how many apples he has...but we know better - because of the right side! There are two apples that Mr. x has. But things do get weird...

Suppose Mr. X and Ms. Y are traveling with 5 apples; but we don't know whose apples belong to who - (does it matter...well, if you want more apples, it does...) The possibilities are X having 0,1,2,3,4,5 apples and likewise for Y having 0,1,2,3,4,5. But the thing is...the total needs to be 5...so...if Mr. X has no apples, then Ms. Y must have 5; if Mr. X has 1 apple, then Ms. Y has to have 4, and so on...this can be graphed on a Cartesian plane as a line, since on this equation, there are quite a few answers. We'll leave Mr. X and Mr. Y alone so they can make babies...just kidding.

Let's take this and make it more complex, without it being to confusing...consider a circle. The equation for that is x^2 + y^2 = r^2, (r is the radius of the circle, and ^ means something times that same something). Let's make r = 4 to make this a little more headache proof... Now, Note this: In our case, if x = -1, then (-1)(-1) is positive, because the opposite of negative is positive (the opposite of no is yes, or I'm not not going means, I'm going). The same goes for y = -1. Now, if we were to say that x = 1, then we would have:

(1)(1) + y^2 = 4 or, to find out what y^2 is...we have to take 1 away from both sides, and then...

y^2 = 3; but that means (y)(y) = 3...what shall we do? Well, thank goodness, some crazy mathematician (probably on drugs) came up with the square root idea which takes the square root of a number or variable; for example the square root of 9 is 3, and the square root of 4 is 2. But something weird happens in algebra:

The square root of something squared is ALWAYS the positive and negative number! Why? Because of the order of things. We know that (2)(2) is 4, and also (-2)(-2) is 4, so there are two possible answers to x^2 = 4. When you take the square root of both sides, those two answers still hold true, since the square root of x^2 is x, and since (-x)(-x) = x, then the square root of x^2 is also (-x). Beware! The square root of any number (not being squared intentionally) is ONLY the positive answer though. So the square root of 9 is only 3; yet the square root of 3^2 is both 3 and -3. So, by taking the square root of y^2 = 3, we have two answers: The square root of 3 and the negative square root of 3. Let's note something...that I only plugged in one number for x and I got two values for y. Why? Because this is crucial in understanding the answer to your question.

Now, here is where your question comes in. What is a function? A function is a rule that states this (yeah, fellow mathematicians, I'm not stating the actual definition...blah blah blah...):

For every x in this equation, you can only have one value for y. So, one value of x cannot have two or more different values of y. It is true that you can have this situation though...x = 2 and y = 5 and x = -2 and y equaling 5, since two different x's have exactly one answer for y (not 5 and -5). So let's look at that circle again...

Note that we had for x = 3, two different answers for y: the square root of 3 and the negative square root of 3. Something wrong here...Mayday Mayday! Call the National Guard....I don't know what to call them, but call them anyway!! ! That circle is not a function!! ! Because one x produced two different y's! Launch the nuclear weapons, and get me a psychologist, because I'm actually having fun doing this? lol

To sum it up, the difference between an equation and a function is this: In an equation, you can have as many answers as you want for one particular x on the left side of the equation, but in a function, you can only have one answer for each particular x.

I hope that helped you, Salome. If not, please let me know, and I'll try another way to explain it.

You may be in for a case on unrequited love. mathematics whether you like it or hate it has a purity about it that requires the utmost in logical skill. Following a difficult proof is... well. its difficult. Coming up with a proof for a deep theorem is even harder than following someone else's proof. Solving a problem requires that the solver get to the heart of the problem and ignore the irrelevant. These are tough standards and there is no way of making them easy. That is why so few people study and even do mathematics professionally. It is by its nature a minority undertaking. However, you can still appreciate the beauty of mathematical structures even if you cannot build them. Most of us can appreciate art, even if we do not have much talent for it.

I love music, but I have a hard time carrying a tune and I am a musical illiterate. I can only read a score in the key of C.

ruveyn

While most of your explanation sounds OK, this part is a bit fuzzy. The square root is a function defined on non-negative numbers, on which it always yields exactly one value, no matter if the radicand is the result of some other number being squared. For example, sqrt((–3)²)=3, so sqrt(x²) for real values "x" is actually the absolute value of "x", namely "|x|".

Now when it comes to rearranging equations, you need to be careful. The good news is that the square root is a one-to-one correspondence between non-negative numbers, so the resulting equation will be equivalent to the original equation. But when you apply the square root to (x–2)²=4 (which is possible because 4≥0), you need to be aware that the result is NOT x–2=2, but |x–2|=2, as explained above. To solve that further, you need to consider two cases:
1. Assume that x–2≥0. Then |x–2|=2 is equivalent to x–2=2, or x=4. As 4–2>0, x=4 is a valid solution.
2. Assume that x–2<0. Then |x–2|=2 is equivalent to –(x–2)=2, or x–2=–2, or x=0. As 0–2<0, this is also a solution.
Now that we've covered all possible cases, x=4 and x=0 are the only solutions possible.


I agree. While it's perfectly OK to read and enjoy "math explained in simple terms" books, arguing about it is futile if one doesn't know the precise definitions.
For example, I don't think it's possible to understand the identity 0.999...=1 without knowing limits. There are many good "common sense"-based explanations, but they can all be refuted by clever rhetorics, leading to pointless discussions about something that doesn't need to be discussed because it's an immediate consequence from the formal definition.

That is correct. One must know what a sequence is, what a series is and what convergence to a limit is. If I had a dollar for every piece of nonsense about 0.999... = 1 I found on the web, I would be a rich man. There is only one right way to look at it, convergence to a limit.

ruveyn

Thank you for your explanations!
Dhp, you made me laugh! So congratulations in making math fun I also understood most of what you wrote.
Vectorspace! You're obviously one of those mathematical geniuses or at least semi geniuses. I understood most of what you wrote as well.
I really appreciate you both taking the time to explain this to me.
I'm working on putting something together to tell you what I've learned so far or rather what I think I've learned.
Point being to see if I've understood things correctly or not.

Grrr I'm stuck again.

Remember the problem I put on here?

I just don't understand how to proceed after step three which I think should have looked like this



[img][800:576]http://farm6.staticflickr.com/5342/9169389715_5e90af8a6d_b.jpg[/img]

Ok so I've figured out that it must be the wrong operation to do for that type of equation. I've realized that this is what should be done. I'm not sure how it's supposed to be written out.




But according to my books this is what is supposed to be done



But that must be an operation for some other type of equation right?

This one is correct. So, you want to solve:

The first thing to do: divide everything by 2, so it "fits" the form of the solution method:

Then you have so

If you calculate that, you get:

But see thats the thing, I don't. How does 9/4 =5?
I'm sorry if I'm hopeless!

Well, you could just type the expression above in a calculator, but I'm glad that you're trying to understand it. So this is the long version: