A one-to-one correspondence of a set A with a set B. The sets A and B are then said to be equinumerable, equipotent or equivalent.

If operations such as addition or multiplication are defined for A and B, it is required that these correspond between A and B.

Two groups are said to be isomorphic if there exists a map f: G₁->G₂ such that f is a bijection. Let G₁ be (G,+) and let G₂ be (H,*), where G and H are arbitrary non-empty sets and + and * are arbitrary operations on those sets. For g₁, g₂ in G, f(g₁ + g₂)
= f(g₁) * f(g₂) => G₁ and G₂ are isomorphic.

I`so*mor"phic (?), a.

Isomorphous.

© Webster 1913

I`so*mor"phic (?), a. (Biol.)

Alike in form; exhibiting isomorphism.

© Webster 1913