Hi Maths;

I am taking your course, I have had 3 College algebra courses already but I am glad to help you check it. Hope people that are being exposed to it for the first time take it also.

Hi Maths;

I am here at the bottom.

http://www.mathsisfun.com/rational-numbers.html

Is that the newest Pythagoras story. I have read at least 6 or 7 different renditions of that. I think this one is pretty good. Hippasus got what he deserved. If only they hadn't discovered those darn irrational numbers. Why couldn't they have just defined that hypotenuse as almost 3 / 2 units? Probably wouldn't have needed square roots and all that i jazz either.

Hi MathsisFun;

I am here:

http://www.mathsisfun.com/algebra/degre … ssion.html

Near the bottom:

You can sometimes work out the degree of an expression by dividing ...

I like the idea of numerical experimentation as a means of getting an answer that can later be proved rigorously.

I noticed that you use 2,4,10,100,1000... to try to determine the limit of ln (3 + √ x) / ln(x). I got embarrassed once when I did the same procedure to guess at a limit. Because I used all even numbers my limit appeared to converge on 1 / 2. What I didn't see was that for odd values it converged to - 1 / 2. Using all even numbers for x ( doesn't matter in your example ) can cause sign errors. So putting some odd numbers in there eliminates that possibility.

Really nice animations!

The decomposing the cube into 4 cuboids was really cool. So far, so good.

http://www.mathsisfun.com/algebra/zero- … perty.html

The "Zero Product Property" says that if a times b is 0, then a  or b has to be 0:

You could include "or both."

http://www.mathsisfun.com/algebra/theorems-lemmas.html

A Lemma is a small results (less important than a theorem)

Possible typo; results -> result

Gee, I prefer the normal definition ... it works the same above and below zero.

Wolfram say their definition "has the benefit that frac(x)+int(x)=x". Well the normal definition has the benefit that frac(x)+floor(x)=x. Seems like they are trying to justify a mistake.

Thanks for pointing this out. I may need to make a special note.

Hi all;

There isn't any general agreement on how to handle frac(-3.65). Most calculators and CAS are in favor of -.65 while most books and sites are favoring .35. A small note to warn the reader about the ambiguity would be a good idea.

Hi MathsisFun;

I think that is enough.

phrontister wrote:

I think it is the way that INT handles negative decimal numbers in different calculators etc that gives the differing results, not necessarily that they use frac(x) = x - int(x).

Oh yeah. How about this:

The "Int" function (short for "integer") is like the "Floor" function, BUT some calculators and computer programs show different results when given negative numbers:

* Some say int(-3.65) = -4 (the same as the Floor function)

* Others say int(-3.65) = -3 (which is the integer closest to zero)

So be careful with this function!


And under "frac" I have:

HOWEVER: many calculators and computer programs use frac(x) = x - int(x), and so their result depends on how they calculate int(x):

Some say frac(-3.65) = 0.35

Others say frac(-3.65) = -0.65

MathsIsFun wrote:

* Others say int(-3.65) = -3 (which is the integer closest to zero)

I reckon this might be better:

* Others say int(-3.65) = -3 (the same as the Ceiling function)

It mirrors the bracketed comment for the -4 case, giving better consistency.

Furthermore, for negative numbers, -1 "is the integer closest to zero", not -3. 

MathsIsFun wrote:

Some say frac(-3.65) = 0.35

Others say frac(-3.65) = -0.65

I'd prefer this, which I think ties it in more clearly with the part that int plays in this:

Some say frac(-3.65) = 0.35 ...... i.e., -3.65 - (-4)

Others say frac(-3.65) = -0.65 ...... i.e., -3.65 - (-3)

Last edited by phrontister (2010-04-21 10:47:22)

Thanks phrontister,

I went for most of your suggestions, but instead of "(the same as the Ceiling function)" I went with "(the rule is: neighbouring integer closest to zero, or "just throw away the .65")", as that is the rule they follow for positive and negative.

We have kept it short, sweet and hopefully accurate

Hi;

I was just mentioning it so that you would know, if you think you should change it then:

The relationship looks like this:

So when [H+] is 10^(-7) then - log (10^-7) = 7 a neutral ph. As [H+] goes up [OH-] goes down.

You can use either of these for accuracy.

Use either of those just as long as in your opinion it does not confuse the reader.
Just phrase it as - log of the molar concentration of the hydronium ion or the hydrogen ion for H30+ or H+ respectively. You see in math [ ] is for grouping but in chemistry [ ] this means molar concentration( moles per liter ).

Hi MathsisFun;

Went through it. Excellent as a refresher course and for first timers. This was my favorite lesson.

http://www.mathsisfun.com/algebra/circle-equations.html

I was doing it wrong, thanks for helping here.