Fact Check: 2 plus 2 equals 4

10) must contend with two questionable consequences of their views: (1) Although the Earth and the Sun were around long before humans and other animals were, the fact that two plus two equals four was not.

Only in the last two categories does 2 + 2 = 4. Let me explain. ... does is name or classify. Each number merely represents a category or individual. For example, numbers on baseball or football uniforms are only nominal. Having the number "1" on your uniform does not necessarily mean you are ...

In establishing the mundane reality ... 2 + 2 = 4, in De Neutralibus et Mediis Libellus (1652) Johann Wigand said: "That twice two are four; a man may not lawfully make a doubt of it, because that manner of knowledge is grauen [graven] into mannes [man's] nature." In the comedy-of-manners play Dom Juan, or The Feast with the Statue (1665), by Molière, the libertine protagonist, Dom Juan, is asked in what values he believes, and answers that he believes "two plus two equals ...

The identity 2 + 2 = 4 is frequently used for that discussion precisely because it is noncontroversial in all human cultures that have counting numbers and arithmetic up to 4. Which is pretty well all cultures today.

Of course, numbers were discovered centuries before set theory, and historically they were "reversed engineered" back to the axioms of set theory. The proof of 2 + 2 = 4 shows what was involved in that reverse engineering, representing the work of many mathematicians from Dedekind to von Neumann.

Description: Two plus two equals four. For more information, see "2+2=4 Trivia" on the Metamath Proof Explorer Home Page: mmset.html#trivia. This proof is simple, but it depends on many other proof steps because 2 and 4 are complex numbers and thus it depends on our construction of complex numbers.

Finally, there are two important successor-axioms we need to know to prove 2 + 2 = 4: A1: ∀x(x + 0) = x A2: ∀x∀y(x + sy) = s(x + y) So the proof that 2 + 2 = 4 is the following: ... (ss0 + ss0) = ssss0 by Transitive Equality on 5 and 7 ...

Accurate measures will repeatedly, positively indicate that adding two quarts and two quarts of water does not yield four. For cooking purposes, the difference may not be critical. For scientific purposes, the difference can be critical. Even for cooking, if the water is left to sit a while, ...

And if you claim otherwise that can understandably upset some people. For example, the mathematician Kareem Carr recently got fire on twitter for pointing out that 2+2 isn’t always equal four.