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Math and Arithmetic

What is a trivial truth?

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October 06, 2010 10:47AM

A trivial truth is a term used for an implication that is true for all cases, regardless of what implies it.

That is, a statement in the form "If P then Q" is trivially true when Q is always true, regardless of P.

eg.

the statement "If x < -3, then x^2+1 > 0" is trivially true, because no matter the truth outcome of x<-3 (which could be true or false depending on the value of x), x^2+1 will always be greater than zero, as x^2 will always be greater than or equal to zero.