What does ∏ mean and how can i use it? (2024)

http://en.wikipedia.org/wiki/Infinite_product

http://mathworld.wolfram.com/InfiniteProduct.html

Short answer - you are exactly correct. Read it exactly as you would a summation sign, but change the operation to multiplication.

So, for a really boring example, you had, for example, [itex]\displaystyle\sum\limits_{i=0}^3 i^3[/itex] it would be [itex]0^2 + 1^2 +2^2 + 3^2= 0 + 1 + 9 = 10[/itex]

But if I changed that to [itex]\prod_{i=0}^3i^2[/itex] it would be [itex](0^2)(1^2)(2^2)(3^2)=0[/itex]

Probably less boring if I didn't make it start from zero, but you get he idea. It's a very different answer! (Also note that the formatting is usually the same, with the i=0 and the 3 above and below the sign respectively. For some reason it didn't format that way here. But generally the notation is very similar.

-Dave K

dkotschessaa said:

For some reason it didn't format that way here.

That's because you used inline math mode for one, display mode for the other.

Display mode:
[tex]\prod_{i=0}^3 i^2[/tex]
[tex]\sum_{i=0}^3 i^2[/tex]

Inline: [itex]\prod_{i=0}^3 i^2[/itex] versus [itex]\sum_{i=0}^3 i^2[/itex]

Thanks guys :)

isnt there also a upside down one of ∏ these? is that the exact opposite? meaning that it is always division instead of multiplication?

I don't think I've ever seen an upside down Pi, but maybe you mean

[tex]\bigcup[/tex]

which is from set theory and has nothing to do with the product symbol.

micromass said:

See Also

Pi Is Encoded in the Patterns of Life

There is the symbol ##\coprod##.

I am familiar (intimately so) with upside-down cake. But this is the first time I'm hearing of upside-down pi.

Curious3141 said:

I am familiar (intimately so) with upside-down cake. But this is the first time I'm hearing of upside-down pi.

http://instantrimshot.com/

micromass said:

There is the symbol ##\coprod##.

How does that symbol work? I'm very curious to find out. It probably won't make any sense seeing as how I've never studied abstract algebra

Vacrin said:

How does that symbol work? I'm very curious to find out. It probably won't make any sense seeing as how I've never studied abstract algebra

In some sense, it is the "dual" of the product ##\prod##. It is defined as such in category theory. The general definition probably won't make sense to you. But if you know sets, then we can define it as the disjoint union. That is, we define

[tex]\coprod_{i\in I} A_i = \bigcup_{i\in I}( A_i\times \{i\} )[/tex]

Informally, we just take the union of the sets ##A_i##, but we force them to be disjoint by taking the cartesian product with ##\{i\}##.