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(There are defined concepts such as the [[surreal number]]s and the [[ordinals]] where operations on infinite objects are well defined.)
==Logical circularity==
In some cases it may constitute [[circular reasoning]] to use L'Hopital's rule to evaluate such limits as
:<math>\lim_{h\to 0}{(x+h)^n-x^n \over h}.</math>
If one uses the evaluation of the limit above for the purpose of ''proving'' that
:(''d''/''dx'') ''x''<sup>''n''</sup> = ''nx''<sup>''n''−1</sup>
and one uses L'Hopital's rule and the fact that
:(''d''/''dx'') ''x''<sup>''n''</sup> = ''nx''<sup>''n''−1</sup>
in the evaluation of the limit, then one's reasoning is circular and therefore fallacious.
[[Category:Mathematical analysis]]
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