One reason that it can be important to identify the precise assumptions that go into a proof—even though some of these assumptions could be perfectly ‘obvious’ things—is that mathematicians are frequently interested in other kinds of entity than those with which the proof might be originally concerned. If these other entities satisfy the same assumptions, then the proof will still go through and the assertion that had been proved will be seen to have a greater generality than originally perceived, since it will apply to these other entities also. On the other hand, if some of the needed
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