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We don’t use the term “range” much here, and I explained why.
Of course, whether or not you need replacement to define the range of a function depends on the definition of “function”. If “function” means “set of ordered pairs” then it always has a range. It’s only if “function” means a class of ordered pairs that you need replacement.
Right, I tried to make that clear in the last paragraph. But maybe the first paragraph should also be clarified.
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