The absolute value (|5|) numbers are 5 and -5.
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This would be the mean, which is what is usually meant by the average of the values.
Because there are numerical values which cannot be expressed as ratios of two integers. That is, there are numbers that are not rational.
A logic operation is when you work with the truth or falsehood of statements whereas an arithmetic operation is concerned only with numerical values.
Well, honey, the least numerical value is negative infinity. It's like the Kardashians' relevance - it just keeps getting smaller and smaller. So, if you're looking for the tiniest number on the number line, negative infinity is your guy.
The whole point of a nominal variable is that is has no numerical value associated with it. With a binary measure you can allocated the values 1 and 0 or +1 and -1 for observations where the attribute is present or absent. If there are more than 2 values that the nominal variable can take then you can allocate any numbers that you want but in all cases the numbers do not have a value: they are simply symbols which can help for sorting and for binary comparisons.