Isomorphisms

Isomorphisms are a way to show that two structures are fundamentally the same, even if they look different. Imagine two different puzzles with separate pieces; if you can rearrange one puzzle's pieces to exactly match the other, they are isomorphic. In mathematics, this means there's a one-to-one correspondence between their parts and how these parts relate. So, an isomorphism indicates the two structures have the same form or pattern, just expressed differently. It helps us recognize when different systems are essentially the same in structure and behavior.