Semigroups and monoids (intro)
General · Mathematics
Study notes
Q: Is (ℕ,+) a monoid? What about (ℕ,×)? Strings under concatenation? (ℕ,+): associative ✓, identity 0 ✓: MONOID! (ℕ,×): associative ✓, identity 1 ✓: MONOID! (Strings, concat): associative ✓, identity "" (empty) ✓: MONOID! (ℕ,+) is NOT a group (no inverses: 3+? = 0 impossible!)!