infinite group

In mathematics, a group is a set of elements with a defined operation (like addition or multiplication) that follows specific rules: closure, associativity, an identity element, and an inverse for each element. An infinite group is a group with an unlimited number of elements. These groups are fundamental in abstract algebra and have applications in various fields like geometry, physics, and chemistry. The concept of infinity itself, meaning something without limits, is explored in mathematics, physics, and metaphysics. While mathematical infinities can be precisely defined and compared, physical infinities remain largely theoretical.123