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### Multiplication or the summation operator (sigma)

Posted: Thu Sep 01, 2011 5:14 pm UTC
Which mathematical concept do you like more? Make sure you don't confuse addition and summation since they are different. Since my last topic comparing opinions on mathematical concepts (lines and curves) went so well I decided to make another one. If this one goes well as well maybe I will make another one in about a week. Idea requests for my next topic are welcome.

### Re: Multiplication or the summation operator (sigma)

Posted: Thu Sep 01, 2011 8:03 pm UTC
What?

### Re: Multiplication or the summation operator (sigma)

Posted: Thu Sep 01, 2011 8:23 pm UTC
I don't know which concept I like more, but summation is more versatile than multiplication. Summation can completely replace multiplication, as if you want xy for some constants x and y, you can just do a summation of y x times (or vice versa). However, with summation, you can do things like sum (n+1), with n going from 1 to 8, and you just don't get that with multiplication.

### Re: Multiplication or the summation operator (sigma)

Posted: Thu Sep 01, 2011 9:28 pm UTC
Anonymously Famous wrote:Summation can completely replace multiplication

Only if you allow non-integer numbers of iterations (in which case, I'd argue that it's no longer been reduced solely to summation as you need some notion of non-integer iteration).

### Re: Multiplication or the summation operator (sigma)

Posted: Thu Sep 01, 2011 10:02 pm UTC
gmalivuk wrote:What?

Pancakes v. waffles for people slightly more mathematically minded.

I think. I can't really tell, either.

### Re: Multiplication or the summation operator (sigma)

Posted: Thu Sep 01, 2011 10:13 pm UTC
Otter?

### Re: Multiplication or the summation operator (sigma)

Posted: Fri Sep 02, 2011 3:31 am UTC
eSOANEM wrote:
Anonymously Famous wrote:Summation can completely replace multiplication

Only if you allow non-integer numbers of iterations (in which case, I'd argue that it's no longer been reduced solely to summation as you need some notion of non-integer iteration).

You are, of course, correct. I'd neglected to consider non-integer multiplication. Silly me. As long as one is an integer, though, it still works. If not... Well, it can take the place of multiplication in several instances, so it's still pretty cool.

### Re: Multiplication or the summation operator (sigma)

Posted: Fri Sep 02, 2011 4:18 am UTC
Macbi wrote:Otter?
Good point.

### Re: Multiplication or the summation operator (sigma)

Posted: Fri Sep 02, 2011 5:25 am UTC
gmalivuk wrote:
Macbi wrote:Otter?
Good point.

We're not talking about points until next week.

### Re: Multiplication or the summation operator (sigma)

Posted: Fri Sep 02, 2011 5:36 am UTC
Anonymously Famous wrote:I don't know which concept I like more, but summation is more versatile than multiplication. Summation can completely replace multiplication, as if you want xy for some constants x and y, you can just do a summation of y x times (or vice versa). However, with summation, you can do things like sum (n+1), with n going from 1 to 8, and you just don't get that with multiplication.

Not in Galois fields you can't!

### Re: Multiplication or the summation operator (sigma)

Posted: Fri Sep 02, 2011 6:05 am UTC
Anonymously Famous wrote:However, with summation, you can do things like sum (n+1), with n going from 1 to 8, and you just don't get that with multiplication.

What?

$\prod_{n=1}^8 (n+1) = 9!.$

I otter ducked... this question sucks.

### Re: Multiplication or the summation operator (sigma)

Posted: Fri Sep 02, 2011 6:12 am UTC
I think that, on balance, I much prefer ducks to curtains. I'm open to being convinced, though.

### Re: Multiplication or the summation operator (sigma)

Posted: Fri Sep 02, 2011 6:31 am UTC
Everyone needs their privacy. Quacking is a luxury. Ergo, curtains.

### Re: Multiplication or the summation operator (sigma)

Posted: Fri Sep 02, 2011 7:33 am UTC
[imath]\ln\left(\prod x_n \right) = \sum \ln\left( x_n \right)[/imath]

### Re: Multiplication or the summation operator (sigma)

Posted: Fri Sep 02, 2011 8:39 am UTC
dissonant wrote:
[imath]\ln\left(\prod x_n \right) = \sum \ln\left( x_n \right)[/imath]

Actually it's not exactly true

Spoiler:
every [imath]x_n[/imath] need to be positive

### Re: Multiplication or the summation operator (sigma)

Posted: Fri Sep 02, 2011 8:58 am UTC
Tryss wrote:
Spoiler:
every [imath]x_n[/imath] need to be positive

Actually it's not exactly true
Spoiler:
You can define the logarithm on the complex plane (except 0), as long as you are careful about +- 2 pi n

[imath]\ln\left(|\prod x_n| \right) = \sum \ln\left( |x_n| \right)[/imath] to remove all problems.

### Re: Multiplication or the summation operator (sigma)

Posted: Fri Sep 02, 2011 11:25 am UTC
The OP made a big thing about not confusing addition with a summation... presumably the same distinction applies to multiplication vs sequence products. So we're comparing the multiplication of a number of individually-specified terms, with the sum of a sequence of values.

Hence my comparison with the "curtains or ducks" bit.

### Re: Multiplication or the summation operator (sigma)

Posted: Fri Sep 02, 2011 1:46 pm UTC
Ugh sometimes I really hate mods. Just so you know I did not put that "otter" option into the poll. I edited the poll again to return it to its original state.

### Re: Multiplication or the summation operator (sigma)

Posted: Fri Sep 02, 2011 3:02 pm UTC
scratch123 wrote:Ugh sometimes I really hate mods. Just so you know I did not put that "otter" option into the poll. I edited the poll again to return it to its original state.

Otter option IS best option.

### Re: Multiplication or the summation operator (sigma)

Posted: Fri Sep 02, 2011 3:21 pm UTC
scratch123 admits to tampering with the otter vote, and once again democracy fails. For shame....

### Re: Multiplication or the summation operator (sigma)

Posted: Fri Sep 02, 2011 3:51 pm UTC
I voted for dinosaurs.

### Re: Multiplication or the summation operator (sigma)

Posted: Fri Sep 02, 2011 5:00 pm UTC
scratch123 wrote:Ugh sometimes I really hate mods. Just so you know I did not put that "otter" option into the poll. I edited the poll again to return it to its original state.
If you don't want me adding foolish options to your polls, might I suggest you find things to post about other than foolish polls?

### Re: Multiplication or the summation operator (sigma)

Posted: Fri Sep 02, 2011 5:13 pm UTC
Clearly the summation operotter.

### Re: Multiplication or the summation operator (sigma)

Posted: Sun Sep 04, 2011 1:01 am UTC
scratch123 wrote:Idea requests for my next topic are welcome.

How about "Ridiculous poll" or "Pointless poll" you can then use those results for the poll after that.

### Re: Multiplication or the summation operator (sigma)

Posted: Fri Sep 09, 2011 1:58 pm UTC
gmalivuk wrote:
scratch123 wrote:Ugh sometimes I really hate mods. Just so you know I did not put that "otter" option into the poll. I edited the poll again to return it to its original state.
If you don't want me adding foolish options to your polls, might I suggest you find things to post about other than foolish polls?

Whats so foolish about it? Are you not allowed to have opinions about abstract concepts?

### Re: Multiplication or the summation operator (sigma)

Posted: Fri Sep 09, 2011 2:22 pm UTC
You can have opinions on anything you want. That's not the same as wanting to create a silly poll about every single one of them. If you don't actually have something mathematical to discuss, I fail to see why you need to create a thread in the mathematics forum.

Also, who are you to declare that my opinion about an abstract concept cannot be "otter"?

### Re: Multiplication or the summation operator (sigma)

Posted: Fri Sep 09, 2011 3:18 pm UTC
gmalivuk wrote:You can have opinions on anything you want. That's not the same as wanting to create a silly poll about every single one of them. If you don't actually have something mathematical to discuss, I fail to see why you need to create a thread in the mathematics forum.

Also, who are you to declare that my opinion about an abstract concept cannot be "otter"?

So is making polls discouraged here or something? Polls do give you something to discuss since in addition to voting you can give reasons as to why you think that way. I think talking about the subjective parts of math is important.

### Re: Multiplication or the summation operator (sigma)

Posted: Sat Sep 10, 2011 5:54 am UTC
scratch123 wrote:So is making polls discouraged here or something?

This poll, and the lines and curves one, seems almost troll-y to me though. You give very little context on what exactly you are wanting people to compare about two topics both of which are fundamental and (one could argue) indispensable.

Spoiler:
New Poll!

What would you rather stop doing? Breathing? Or having a pulse?

See what I mean?

### Re: Multiplication or the summation operator (sigma)

Posted: Sat Sep 10, 2011 4:55 pm UTC
Duck.