Intuition
The purpose of defining a group homomorphism as it is, is to create functions that preserve the algebraic structure. An equivalent definition of group homomorphism is: The function h : G → H is a group homomorphism if whenever we have . In other words, the group H in some sense has a similar algebraic structure as G and the homomorphism h preserves that.
Read more about this topic: Group Homomorphism
Famous quotes containing the word intuition:
“When a scientist is ahead of his times, it is often through misunderstanding of current, rather than intuition of future truth. In science there is never any error so gross that it won’t one day, from some perspective, appear prophetic.”
—Jean Rostand (1894–1977)
“All appeared new, and strange at first, inexpressibly rare and delightful and beautiful. I was a little stranger, which at my entrance into the world was saluted and surrounded with innumerable joys. My knowledge was divine. I knew by intuition those things which since my Apostasy, I collected again by the highest reason.”
—Thomas Traherne (1636–1674)
“Well, intuition isn’t much help in police work. Facts are what we need.”
—Crane Wilbur (1889–1973)