Any example of making a collection of sets as a group?(adsbygoogle = window.adsbygoogle || []).push({});

Let's say, we have a collection of sets, called H. Each element of H is a set, and it works as a group element. So we have a group H whose elements correspond to sets.

The group can be constructed easily for some trivial cases.

For instance, H = {...,{-3}, {-2}, {-1}, {0}, {1}, {2}, {3},,,}, where H consists of single-element sets and each {x} corresponds to an integer x∈Z.

addition : {a} + {b} = {c} (a,b,c ∈ Z}

identity : {0}

inverse of {a} = {-a}

When I tried to make a collection of different size of sets, I couldn't figure out how to define multiplication (or addition), identity and inverse on sets for group operations.

Any advice or example?

Thanks in advance.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Making a collection of sets as a group

**Physics Forums | Science Articles, Homework Help, Discussion**