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### Are all statements about math inherently formal? Can one do math without formal logic? [duplicate]

Are all people who do mathematics applying (whether they know it or not) formal logic? Does every statement someone may make about math, at its core, a formal statement in mathematical logic? (I'm ...
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### Still struggling to understand vacuous truths

I know, I know, there are tons of questions on this -- I've read them all, it feels like. I don't understand why $(F \implies F) \equiv T$ and $(F \implies T) \equiv T$. One of the best examples I ...
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### Why is "A only if B" equivalent to "(not A) or B"? [duplicate]

I've encountered this recently and I just can't wrap my head around it. My book states that $$A \rightarrow B \equiv \neg A \lor B$$ It's my understanding that $A \rightarrow B$ means that if $A$ ...
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### If $\lim_{x\to 0}f(x)=L$ then $\lim_{x\to 0}f(cx)=L$ for any nonzero constant $c$.

I was just wondering if this proof is correct. I'm trying to prove that if $\lim_{x\to 0}f(x)=L$ then $\lim_{x\to 0}f(cx)=L$ for any nonzero constant $c$. Proof: If $\lim_{x \to 0}f(cx)=L$ ...
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### Are there important situations where we study false statements as if they were true?

I know of two situations resulting from asserting that a false mathematical statement is true (by this we assume that the statement has been made to be a mathematical axiom and that it must be true ...
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### "If P, then Q; If P, then R; Therefore: If Q, then R." Fallacy and Transitivity

Two fallacious arguments: If P, then Q If P, then R Therefore: If Q, then R And If P, then Q If R, then Q Therefore: If P, then R However, if these particular propositions were interpreted as ...
861 views

### What is a good example to show high school students why a proof for induction is a reasonable kind of proof?

I teach average-level high school students who have not had much beyond Algebra 1. I want to show them why induction makes sense. I want the sort of problem where it is intuitive that a statement is ...
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1 vote
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### Intuitonism and metamathematics.

There are various reasons why one would want to reject the law of the excluded middle when doing "normal" mathematics, which I won't get to here, but accepting those, does the same reasoning hold when ...
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213 views

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