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[ZetaX]

I would try to avoid using the sarcasm mark. It shows up as a broken character on a very significant proportion of computers/fonts.

I have seen several persons that said exactly the same in full sincerity. And judging from the reponses at least some here are serious about tthat.
Next time either say the intended thing or add some sarcasm tag; or at least don't respond like it is "obvious" that it is when it really isn't.

[bahihs]

This is talking about the denumerability of the rational number system, I don't see how that doesn't fall into number theory. Although its kinda a trivial argument...

The denumerability is a set theoretic property. Nothing number theory is really concerned about. Obviously, set theory is. Why would you associate it into a field that does not care about this instead of the field that is by definition concerned with the question¿
Edit: Additionally, this is not really about the rational numbers, but about denumberability of finite products of denumerable sets. And the denumberability of their subsets. See, no mentioning of the rationals at all.

*shrugs* Sounds good to me. I don't have the credentials to argue otherwise, I'm just stating what the book says.

[Baffler]

Nevermind, I remembered a few seconds after I pressed post.

[Reelya]

I would try to avoid using the sarcasm mark. It shows up as a broken character on a very significant proportion of computers/fonts.

I have seen several persons that said exactly the same in full sincerity. And judging from the reponses at least some here are serious about tthat.
Next time either say the intended thing or add some sarcasm tag; or at least don't respond like it is "obvious" that it is when it really isn't.

Umm... he/she didn't say anything about the content of your post whatsover, just that the sarcasm symbol you used doesn't work for many users (there's also no universal convention that that means irony either). So they won't get what you mean anyway. Try /sarc instead or something that can be viewed by all users.

[ZetaX]

I would try to avoid using the sarcasm mark. It shows up as a broken character on a very significant proportion of computers/fonts.

I have seen several persons that said exactly the same in full sincerity. And judging from the reponses at least some here are serious about tthat.
Next time either say the intended thing or add some sarcasm tag; or at least don't respond like it is "obvious" that it is when it really isn't.

Umm... he/she didn't say anything about the content of your post whatsover, just that the sarcasm symbol you used doesn't work for many users (there's also no universal convention that that means irony either). So they won't get what you mean anyway. Try /sarc instead or something that can be viewed by all users.

Ah, now I understand what this was about. No, that wasn't supposed to be a sarcasm mark at all. Yes, the sentence was somewhat sarcastic in its meaning, but can also be taken at face value without problems, so I didn't bother. That reverse question mark (it's the spanish one) is just a pet peeve of mine. Sorry for the confusion.

[3man75]

I'm currently doing lines and rational expressions. Stuck on two different problems for both and rationals are really kicking my a$$.

For rational expressions i'm stuck on something thats like:

1+1
     x
-----------
1-1
   x

That is 1 plus 1 over x. All of that is over 1 minus 1 over x.

I just have no idea how to deal with fractions this way...

The second one is a line probelem where the problem gives you two points (-3,4) and (2,5). I'm suppose to "express your answer using either general form or slope intercept form.". I imagine getting the slope but that I can do using Y2 - Y1 over X2 - X1.

[3man75]

Hard to say since I can't understand all of the symbols.

The answer the book gives is:

x + 1
------
X - 1

Not sure if that's what you have their. I'm looking for how to actually do the work behind these problems.

[i2amroy]

x/(x-1) + 1/(x-1) does indeed equal (x+1) / (x - 1), which is what your book gives there.

Hard to say since I can't understand all of the symbols.

Any particular symbols you seem to be having problems with?

[Helgoland]

What you really need to internalize is that you can always add parentheses, and that you can treat all the stuff inside a pair of parentheses as just one blob.
Example: (1 + 1/x)/(1 - 1/x)
Let's look at the two blobs, (1 + 1/x) and (1 - 1/x). First things first:

(1 + 1/x)
= 1*(1 + 1/x) Well, multiplying by one doesn't change anything
= x/x * (1 + 1/x) And x/x = 1, so I'm allowed to write it like this
= 1/x * (x + x/x) Here I just pull the upper x inside the parentheses
= (x + 1)/x Because x/x = 1. For convenience I pulled the 1/x to the end,

Similarly we get that (1 - 1/x) = (x - 1)/x. (This you should do as an exercise! It's the same steps as above, but it'll help you to write it out yourself.)

So now we can go back to the original problem:
(1 + 1/x)/(1 - 1/x)
= ((x + 1)/x)/((x - 1)/x) I just wrote the two blobs in a different way, as seen above - this doesn't change anything
= 1*((x + 1)/x)/((x - 1)/x) Multiplying with one doesn't do anything, see above
= x/x*((x + 1)/x)/((x - 1)/x) And we can do this because x/x = 1, as above
= (x*(x + 1)/x))/(x*(x - 1)/x) I just pulled together the two fractions - if you write it down by hand, this is very intuitive
= (x + 1)/(x - 1) Because the x's inside the two blobs cancel out each other

You should write down all that by hand, in proper notation - it's next to impossible to really see anything the way I had to write it here. Once you've done it as above a couple times, you'll notice that you can do most of the steps in your head - so it won't always be as much of a pain in the ass as the stuff above


Any questions? I tried to be fairly explicit and clear, but I have a nasty habit of not living up to these aspirations...

[3man75]

I just can't understand the symbolism on here. When I look at some of these super fractions in the book it can get messy. Here on the forums doubly so.

If anyone can post a note about what is being explained that is game. Not trying to sound ungrateful but I don't know what happened here:  x/x * (1 + 1/x) And x/x = 1,

Are you multiplying 'X' all over the place?

[Helgoland]

The 'And x/x = 1' bit is just commentary - the equation chain is just the stuff on the left, this stuff:
(1 + 1/x)
= 1*(1 + 1/x)
= x/x * (1 + 1/x)
= 1/x * (x + x/x)
= (x + 1)/x

You usually write stuff like this in multiple lines to make it easier to read.



Regarding notation, 'x/x * (1 + 1/x)' means:

Code: [Select]

x                 1
--- *  ( 1 + -----  )
 x                 x


Now - seriously - go write down the equations I posted on paper, in the 'horizontal bar' notation! It'll be much easier to understand then.

[3man75]

Sort of get it. But still struggeling with that and i've sort of had to leave it as is because now were doing lines. I remember doing okay before but I've gotten super rusty. One problem in particular states: parralel to the line y= - 3x; point (-1,2) and write down the answer as y=mx + B or general form (Ax +By=C. If I remember correctly). I don't get what to do any the chapter on it has so many words telling me so many different wierd things.


 I wanted to ask how learnable is the skill known as math? The new major I'm picking up is requiring up to calculas 1, statistics, trigonometry, and discreet math 1.

[frostshotgg]

It's learnable, with varying understanding. Math at that level stops being algebra and starts being heavy duty reasoning/critical thinking. At worst you can get through the class by memorizing the steps to do a given type of problem, but if you learn how stuff works then it becomes a lot easier.

Also Statistics isn't math.

[Arx]

At that level, it basically is.

As for functions, remember that parallel lines have equal gradients (m) and all straight lines must pass through the point (0, c) and you should be able to tackle most problems of that particular nature.

[Reelya]

Sort of get it. But still struggeling with that and i've sort of had to leave it as is because now were doing lines. I remember doing okay before but I've gotten super rusty. One problem in particular states: parralel to the line y= - 3x; point (-1,2) and write down the answer as y=mx + B or general form (Ax +By=C. If I remember correctly). I don't get what to do any the chapter on it has so many words telling me so many different wierd things.


 I wanted to ask how learnable is the skill known as math? The new major I'm picking up is requiring up to calculas 1, statistics, trigonometry, and discreet math 1.

As for the specifc problem: in "y=mx+b", the 'm' constant controls the direction of the line, and the 'b' constant controls the positioning (b moves the line up and down, but doesn't change the direction). If you want parallel lines, they must have the same direction. Therefore m is constrained to -3, and the equation is "y = -3x + b". So this is about the intuition that you can't change "m" and still have the line parallel, so you must use "b" to fix it, since it's the only other variable you have to play with.

So you have an equation that has three unknowns, x,y, and b, and you want to solve for b. This is where the given point comes in. The question requires that the point must pass through (-1,2), i.e. the equation must be true when x = -1 and y = 2. So you can substitute these values in, and solve for b, then use b in your answer:

y = -3x + b
2 = -3(-1) + b
2 = 3 + b
b = -1

Giving you an equation of y = -3x - 1

The final check is to substitute the known point (-1,2) into the equation and check that both sides are equal: 2 = -3(-1) - 1, which is true

I'd say maths is a highly learned skill. It's all about learning how and why things are done, and practice. One of the core skills is about recognizing patterns. That's where "word problems" come in. In a simple sense those "how many people on the bus" questions are about you recognizing that the pattern: X people got on the bus, Y people got off, is all about addition and subtraction. So in applying maths it's about knowing some formulas and being able to ascertain when they are useful.