Mathematical Thinking Stanford, W3

the most difficult lecture

Analysis of language - quantifiers

irrational numbers

∀ for all

∃ there exists

express an existence assertion. a confident and forceful statement of fact or belief.

Combination of quantifiers

there is no largest natural number.

(∀𝑚∈ ℕ)(∃𝑛 ∈ ℕ)(𝑛>𝑚), True

(∃𝑛 ∈ ℕ)(∀𝑚∈ ℕ)(𝑛>𝑚), False

American Melanoma Foundation: “One American dies of Melanoma almost every hour.”

∃A∀H(A dies in hour H), False, misunderstanding: An American dies once every hour, ridiculous.

∀H∃A(A dies in hour H), True

parentheses()