What is the precise definition of, "Differs in exactly one element"?

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The discussion clarifies the precise definitions of "differ in exactly one element" and "differ by exactly one element" in set theory. It establishes that the sets {1,2,3} and {1,2} differ by exactly one element, while the sets {1,2,3} and {1,2,4} differ in exactly one element. The distinction is critical for accurate mathematical communication, particularly in formal contexts where precision is paramount.

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Jarvis323
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Do {1,2,3} and {1,2} differ in, or by exactly one element? Or do those two things mean the same thing. Also, what about {1,2,3} and {1,2,4}.
 
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If you want to be precise use symbols instead of words, but in normal usage:
{1,2,3} and {1,2} differ by exactly one element
{1,2,3} and {1,2,4} differ in exactly one element
 

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