The Real Numbers Are Terrifying

Counting numbers, haha N = {1, 2, 3, . . .} Just two natural numbers! Z = {a − b | a, b ∈ N} Just two integers! Q = {a/b | a, b ∈ Z, b ≠ 0} The limits of infinite convergent Cauchy sequences of rational numbers R = {limₙ→∞ a(n) | a : N → Q, ∀ε > 0. ∃N ∈ N. ∀n > N. |a(n) − a(N)| < ε} Just two real numbers! C = {a + bi | a, b ∈ R}

The meme shows Mr. Incredible explaining increasingly broad number sets: natural numbers, integers, rationals, real numbers, and finally complex numbers. The joke is that the first, second, third, and fifth panels present mathematical constructions as if each set contains only two numbers, while the dark middle panel gives the serious definition of real numbers through limits of Cauchy sequences. It is used as a reaction to escalating mathematical complexity or to mock someone who dramatically overexplains a simple concept.

• @ithueti / 12698 2024-04-29