Finding equations of summations from 1 to a non integer

[Gouskin]

"Just as the English steadfastly rejected Leibnitz's notation -- and fell behind the rest of Europe by more than a century regarding scientific advancements"
--Slippery slope fallacy and anecdotal fallacy

The only reason I'm defending it is because originally I felt insulted by lookagain and defended it a while ago for no other purpose but to just deny him. Now I feel obliged to continue defending it. I don't agree more with one way or another, at this point, it is just a battle to show that I have some kind of will and self-dignity.
But, anyway, complaining about notation in this case is a bit nitpicky, seeing as to how it is clearly obvious in the case of (1/1000000)^2 that the 2 was not floating and was in fact squaring it. The only reason everybody who responded responded the way they did is because they already posted back to me on the same subject and were trying to make a point, otherwise they would have assumed (1/1000000)^2 and answered accordingly. (Please don't use the slippery slope fallacy or the anecdotal fallacy if you reply, thanks!)

 

[mmm4444bot]

it is just a battle to show that I have some kind of will and self-dignity

Whatever toots your scooter!

 

[Gouskin]

Although, now that I think of it, this really isn't a violation of order of operations as order of operations says nothing about this.

It is assumed that you do the operation in the order (10/5)/(10/5) = 1 because there are assumed parentheses implied by the fractional line.
If you used PEMDAS, you would get 10/5/10/5 = 1/25.

 

[Deleted member 4993]

Although, now that I think of it, this really isn't a violation of order of operations as order of operations says nothing about this.

It is assumed that you do the operation in the order (10/5)/(10/5) = 1 because there are assumed parentheses implied by the fractional line.
If you used PEMDAS, you would get 10/5/10/5 = 1/25.

That is why we (the rest of the world excluding you) do NOT express \(\displaystyle \dfrac{\ \frac{10}{5}}{\frac{10}{5}}\ \) as 10/5/10/5

 

[Gouskin]

That is why we (the rest of the world excluding you) do NOT express \(\displaystyle \dfrac{\ \frac{10}{5}}{\frac{10}{5}}\ \) as 10/5/10/5

But PEMDAS/order of operations says one has to, so how can one use PEMDAS/order of operations to argue against the original qualm?

Parentheses come before division. In the case of

, the lack of parentheses is ignored, and it is assumed that it means (5/10)/(5/10)

Parentheses also come before exponents. In the case of

, however, the lack of parentheses is for some reason taken into account and it is now assumed that it is 1^2/1000000 or that is means 1/1000000^2

How does this work? Can you just choose when to and when not to assume parentheses?

 

[JeffM]

But PEMDAS/order of operations says you have to, so how can you use PEMDAS/order of operations to argue against our original qualm?

PEMDAS is a convention, a way of ensuring effective communication. Life would go on just as well as it does today if we all called a table a "mouse" and a mouse a "table," but when virtually everyone has implicitly agreed on how to communicate, a failure to abide by that agreement looks foolish or perverse. You will be unlikely to buy what you want if you try to buy a table trap to cope with rodents.

\(\displaystyle \dfrac{1}{100}\ ^2\) looks strange, perhaps uninformed, and so discourages from people considering your ideas worth engaging.

Furthermore it is ambiguous:

\(\displaystyle \dfrac{1^2}{100} \ne \left(\dfrac{1}{100}\right)^2.\)

Mathematicians have spent a lot of time creating a notation that has meaning globally across linguistic barriers and that avoids much (not all) ambiguity. It is more important to be clear about your ideas than to satisfy your personal standards of aesthetics. Welcome to the adult world.

 

[Gouskin]

\(\displaystyle \dfrac{1}{100}\ ^2\) looks strange, perhaps uninformed, and so discourages from people considering your ideas worth engaging.

Thanks for the good argument.
It has been "fixed."

 

[Gouskin]

So then it becomes impossible to have 5/10/5/10 = .04

So what does one do?
a = 10/5
b = a/5
c = b/10
????????

Can I conclude from the excessive use of question marks and the poorly understood parallelization of a past argument of mine's structure that this is sarcastic in nature and that you are mocking me? (Rhetorical question)

Anyway, let's get off of this stupid syntax stuff and "back to how much I rule" (Maddox).