Fact Check: "1 + 1 = 1"
What We Know
The claim that "1 + 1 = 1" contradicts established mathematical principles. In standard arithmetic, the operation of addition is defined such that the sum of one and one equals two. This foundational concept is supported by various mathematical texts, including Principia Mathematica, where it is explicitly stated that "from this proposition it will follow, when arithmetical addition has been defined, that 1 + 1 = 2" (Wikipedia).
In mathematics, the number 1 is defined as the smallest positive natural number, and it serves as the multiplicative identity, meaning that any number multiplied by 1 remains unchanged (Wikipedia). The operation of addition is governed by specific rules that are universally accepted in mathematics.
Analysis
While there are contexts in which "1 + 1" can yield results that appear to support the claim (such as in certain logical frameworks or abstract algebra), these do not apply to standard arithmetic. For instance, in Boolean algebra, the expression "1 + 1" can equal 1, but this is due to the specific definitions of addition in that system, where the operation represents logical OR rather than numerical addition (YourStatsGuru, YouTube).
The reliability of sources that support the claim is questionable. For example, the article from YourStatsGuru attempts to demonstrate a mathematical error leading to the conclusion "1 + 1 = 1," but it ultimately illustrates a misunderstanding of mathematical operations rather than providing a valid proof (YourStatsGuru). Furthermore, the discussion on Boolean algebra does not apply to conventional arithmetic and should not be conflated with it.
In contrast, the sources that affirm the standard arithmetic definition of addition, such as Principia Mathematica and various educational resources, are well-established and widely accepted in the mathematical community.
Conclusion
The claim that "1 + 1 = 1" is False. It fundamentally misrepresents the principles of arithmetic as defined in mathematics. The standard interpretation of addition clearly states that 1 plus 1 equals 2, and while alternative interpretations exist in specific contexts (like Boolean algebra), they do not apply to conventional arithmetic.