A function is a rule, which assigns one and only one range element to each and every domain element?
I want to answer that this is true but the word "every" is questionable. am i reading too much into this?
The statement about a function being a rule that assigns one and only one range element to each and every domain element is generally true. However, there might be some cases where the word "every" can be questionable or might lead to some confusion.
In mathematics, functions are defined such that for every element in the domain, there is only one corresponding element in the range. This means that each element in the domain is "mapped" to a unique element in the range. In other words, if you have a function f with domain D and range R, for every x in D, there exists exactly one y in R such that f(x) = y.
However, there are certain scenarios where the word "every" might not hold true. For example, if the domain is not defined for certain inputs, then those elements would not be included in the statement "each and every domain element." Additionally, if the range is not fully specified or if it contains duplicate elements, then the one-to-one correspondence might not be maintained.
So, overall, you are correct in being cautious about the word "every" in this statement. While it generally holds true for mathematical functions, there can be specific cases or scenarios where exceptions or ambiguities might arise.