ONE COMMONTRUTH
Truth Library / Mathematics & Physics
OCT-0007 · Mathematical proof

In standard arithmetic, 2 + 2 = 4.

EstablishedSource review: 2026-10-08Revision 2
10 SECONDS

Adding two units to two units gives four. This follows from the definitions of ordinary whole-number arithmetic.

2 MINUTES · CONTEXT & CAVEATS

Show me why

This is a mathematical statement, established by definitions and deduction rather than a survey or experiment. Beginning at 2 and applying the successor operation twice gives 3 and then 4.

A common misconception

Changing the meaning of a symbol or using modular arithmetic does not disprove the statement in its stated system.

Where the limits are

The symbols refer to standard whole numbers and ordinary addition. Other mathematical systems must state their own rules.

DEEP DIVE · FOLLOW THE EVIDENCE

How we know

Let S(n) mean the next whole number. Define addition by a + 0 = a and a + S(b) = S(a + b). Then 2 + 2 = S(2 + 1) = S(S(2 + 0)) = S(S(2)) = 4. Counting objects illustrates this proof but is not its logical foundation.

What would change this conclusion?

Within the stated definitions, the conclusion follows deductively. A different system changes the proposition being discussed.

Sources you can inspect

  1. OpenStax / Rice University
    1.2 Add Whole Numbers — Prealgebra 2e

    Reference for ordinary addition notation; the proof is shown here.

    Publication date not stated · Checked in initial research 2026-10-08

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Revision history

  • Initial AI-assisted source research and scoped explanation. Awaiting owner editorial approval; not publicly verified.
  • Owner explicitly approved all content as created for public publication. Statements, sources and evidence classifications unchanged.
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