Fact Check: 1+1=3

Fact Check: "1+1=3"

What We Know

The claim that "1 + 1 = 3" is mathematically incorrect under standard arithmetic rules. In basic arithmetic, the operation of addition is defined such that the sum of one and one equals two. This is a foundational principle of mathematics, universally accepted across various mathematical disciplines. According to TruthOrFake, the equation "1 + 1 = 2" is a fundamental truth in mathematics, and any assertion that it equals three is incorrect.

Moreover, mathematical proofs, which are logical arguments that establish the validity of mathematical claims, consistently uphold this principle. For instance, formal proofs are constructed using precise rules and syntax, ensuring that all claims made within a proof are justified (Duke University).

While there are discussions and attempts to present scenarios where "1 + 1 = 3" might seem plausible, such as through misinterpretations or manipulations of mathematical principles, these do not hold up under rigorous scrutiny. For example, a YouTube video attempts to illustrate this claim by breaking the rules of mathematics, but it ultimately fails to provide a valid mathematical proof.

Analysis

The assertion that "1 + 1 = 3" can sometimes be encountered in discussions about mathematical fallacies or in contexts that involve abstract or non-standard interpretations of arithmetic. For instance, some sources suggest that in certain theoretical frameworks or under specific definitions, one might arrive at such a conclusion. However, these interpretations are not grounded in conventional mathematics and often involve logical fallacies, such as division by zero or redefining the operations involved (Mathematics Stack Exchange, narkive).

The reliability of sources discussing this claim varies. While academic sources like Duke University provide a solid foundation in formal mathematical reasoning, others, such as the YouTube video ([source-4]) or informal forums, may present misleading or incorrect arguments. The latter often lack the rigor of formal proofs and can lead to confusion rather than clarity.

In summary, while there may be creative or humorous attempts to argue that "1 + 1 = 3," these do not withstand rigorous mathematical scrutiny and are not accepted in any formal mathematical context.

Conclusion

Verdict: False
The claim that "1 + 1 = 3" is false based on established mathematical principles. The assertion contradicts the foundational rules of arithmetic, where the sum of one and one is universally recognized as two. Attempts to validate this claim through unconventional reasoning or manipulation of mathematical concepts do not hold up under critical examination.

Sources

1. 8.5 MATHEMATICAL INDUCTION
2. Automated theorem proving and proof verification
3. Collatz conjecture
4. 1 + 1 = 3 Proof | Breaking the rules of mathematics - YouTube
5. Fact Check: 1+1=3 | TruthOrFake Blog
6. How can 1+1=3 be possible? - Mathematics Stack Exchange
7. Mathematical Induction - Base case above 1 (1 of 3 ...)
8. A proof that 1 + 1 = 3? - narkive