Does this reasoning ever reach infinity? 0<1<2<3<4<5

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The discussion centers around the concept of infinity in mathematics, particularly in the context of the sequence 0<1<2<3<4<5... Participants clarify that infinity is not a number but a concept, emphasizing that mathematical reasoning about numbers approaches infinity rather than reaching it. They explore the implications of the notation used and the nature of mathematical statements, noting that the chain of inequalities represents an infinite series of true statements rather than a finite conclusion. The conversation also touches on the need for rigorous definitions and the potential ambiguities in mathematical notation. Ultimately, the discussion highlights the complexity of understanding infinity within mathematical frameworks.
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Well, it depends on how you define '->' for multi valued logics.

I mean, say we have a logic where every truth value is in [0,1], surely I could then define P -> Q such that P <= Q.

I'm sure we could still derive some interesting things from it.

But I kind of have to plead ignorance on multi valued logics here, so maybe you have a superb reason on why this can't be done.
 

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