Problem Detail: While reading an article on logic, there is a sentence “No number is equal to zero” and we have to assign truth values to this sentence. I hope this is true and the article says it as false. Can someone explain me why it is false? Or the author of the article is wrong?
Asked By : Brainy
Answered By : JiK
It is false if and only if there is a number that is equal to zero. “There is a number that is equal to zero” is true if and only if zero is a number. Without any context (there might e.g. be some very strange definitions given earlier in the exercise), we cannot say whether zero is considered a number in this case. If there is no other context given in the exercise, it should be clear that zero is a number. For example, the domain of discourse might be only positive integers*, when zero is not a number, but then it would be very weird to use the word “zero” in the sentence in the first place. *The set of natural numbers has two contradicting definitions, $mathbb{N}={0,1,2,dots}$ (non-negative integers) and $mathbb{N}={1,2,dots}$ (positive integers). This might be the source of confusion in your case.
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