# Capital $\pi$ notation, i.e $\prod$

There is a step in a proof I don't understand.

$$(\prod_{i\in K} p_{i}^{min(a_{i},b_{i})})\cdot (\prod_{i\in K, 1\leq i\leq k} p_{i}^{min(a_{i},b_{i})}) = \prod_{1\leq i\leq k} p_{i}^{min(a_{i},b_{i})}$$

I'm not so sure what $$\prod_{i\in K}$$ and $$\prod_{i\in K, 1\leq i\leq k}$$ means.

Is there someone who can explain what is going on?

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Are you asking us about what the capital Pi means? Or are you asking us what the set $K$ is? Because for the latter question, I think you just need to look up the definition of $K$ in your context. – TMM Sep 7 '11 at 19:06
This is analogous to the $\sum$ notation for sum: $\sum_{i=1}^3 i^2 = 1^2+2^2+3^2$. – Srivatsan Sep 7 '11 at 19:12

Is $K$ maybe some set of whole numbers, like $K = \{ 1,5,7 \}$? Say we've got a collection $a_1, a_2, \ldots$ of numbers. Then $\prod _{i \in K} a_i$ would mean $a_1a_5a_7$. The second product is over all elements of $K$ between $1$ and $k$. Say $k=6$ and $K$ is as before. Then $\prod _{i \in K, 1 \leq i \leq k} a_i$ is $a_1 a_5$.