Hetware wrote: > [...] If I > choose to interpret (t-3)/(t-3) = 1 for all real numbers, I don't see > how it results in a logical contradiction.
If (t-3)/(t-3) = 1 holds for all real numbers, then (considering the case t = 3) leads to the conclusion that 0/0 = 1. But if / is defined (on the reals, say) so that x/y = z iff x = yz, then 0/0 if it means anything at all can mean all and any real numbers. Since definition is supposed to fix the meanings of symbols not leave them open to meaning everything and anything, 0/0 hasn't been defined. For which reason the proviso y =/= 0 accompanies x/y = z iff x = yz. Since 0/0 hasn't been defined it can't be 1, therefore it isn't true that (t-3)/(t-3) = 1 holds for all real numbers.
Can /some/ meaning be given to 0/0 (outside the reals perhaps?) Maybe, but that won't help with real functions like your F.
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