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# [Solved]: No number is equal to Zero, is this statement true or false?

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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?

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.