Oh, I know the principles and laws of reciprocity, etc

And to me, 6/2n = 6 * (2n)^-1

Heh heh! That is exactly what I am saying. Order of operations: I am completely fine with. It is the things that you are

**operating on **that I am also fine with, but many others are not. They are doing just that: Translating everything into an operator. 2x ? It is 2 x's. 2 cars? yup, 2 cars. We don't say "Hey, did you see the 2 times red cars drive by" ! It is a quantity, just like one mole of something, or a dozen.

24g ÷ 1 mole = 24g ÷ 6.022x10^23

not (24 ÷ 6.022) * 10^23

ab/cd ? (ab)/(cd)

If I wanted abc/c, I write just that.

same for (1/2)x, is x/2

1/2x? 1 ÷ 2x

Just like (6/2)(2+1). I would write that, or i would say 6(2+1) ÷ 2

I apologize if it seems like a little rant

I think it is saying "six divided by 3 x's" and not "6 divided by 3, times x"

As I said, this was the intention of the meaning in 5 schools I went to.

6/3x is/was 2/x, otherwise you write 6x/3, or 2x

Once again a ÷ 1a = ? We both know it is one, but we have brains for a reason, and we know the 1a is a single unit, which translates to 6 ÷ 2n, where '2n' is a single unit, and n is 2+1.

I don't see how anyone can prove that a ÷ 1a = 1 and 6 ÷ 2a = 3a

NOW.... we didn't use calculators in most of my school. It was all on paper, and calculators were forbidden, so we weren't victims of having to input it into a computer. I can't remember when we used them. We had to "prove" all work. When you realize how a computer/calculator interprets things, usually incorrectly, you end up putting ( ) around EVERYthing when you input.

That said, it seems like our discussion is heading in the direction of, how would a computer interpret ..... ?? That is not where I wish it to go, as I care not what computer or program will come up with, or how they will handle the arguments entered.

I am talking about

: "Here is a sheet of paper. Solve this problem showing all work" Having said that, I would never be limited to same size characters on one line across and would hand-write something like this: ½ with a little 'n' right beside the 2.

LOL !! Not another one !! I will pass on that one. I can tell you the first thing that comes to mind, but that is not my "final answer", Regis!

Initial response is "no". not equal. If you use a limit, somehow, with summation and limit of f(x) as x approaching ∞, then the limit could be 1, obviously if f(x) was set up right. been a while since I was in school, so I would have to refresh all areas of that, and I am really not interested right now...

I am almost finished with this one, and it was exhausting, but fun to get 'back in the books'. the annoying part was everyone calling everyone names, etc. Rarely did anyone provide a single reference. Speaking of refs, here is one:

http://faculty.ksu.edu.sa/fawaz/481files/Bartle-Introduction-to-Real-Analysis.pdf
Check out page 53 before and after "or more simply..."

Regards!

MM