Exactly. So we can choose an encoding that is computationally expensive or one which is cheap. The essence
of mathematical thinking is to use replace complexity with simplicity: a person who insists on calculating the sum of positive integers less than n with n - 1 operations is not to be admired for their mathematical insight [their dogged determination may be another matter].
Some encodings are more useful than others while being equivalent. All encoding requires an arbitrary interpretation. Each is equally valid...finding "books" in Pi is a flight of fantasy.
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Exactly. So we can choose an encoding that is computationally expensive or one which is cheap. The essence of mathematical thinking is to use replace complexity with simplicity: a person who insists on calculating the sum of positive integers less than n with n - 1 operations is not to be admired for their mathematical insight [their dogged determination may be another matter].
Some encodings are more useful than others while being equivalent. All encoding requires an arbitrary interpretation. Each is equally valid...finding "books" in Pi is a flight of fantasy.