The natural domain of a formula is the set of values for which it is defined, typically within the reals but sometimes among the integers or complex numbers. For instance the natural domain of square root is the non-negative reals when considered as a real number function. When considering a natural domain the set of possible values of the function is typically called its range.
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“Doubtless, we are as slow to conceive of Paradise as of Heaven, of a perfect natural as of a perfect spiritual world. We see how past ages have loitered and erred. Is perhaps our generation free from irrationality and error? Have we perhaps reached now the summit of human wisdom, and need no more to look out for mental or physical improvement? Undoubtedly, we are never so visionary as to be prepared for what the next hour may bring forth.”
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