[for all of the following, "lim" means the limit as n->∞](adsbygoogle = window.adsbygoogle || []).push({});

Let a_{n}be a sequence of real numbers.

Theorem: if lim a_{n}= L and lim a_{n}= M, then L=M.

(Incorrect) "Proof":

lim a_{n}= L and lim a_{n}= M

Thus, L = lim a_{n}= lim a_{n}= M (transitive property)

Therefore, L=M.

To me, every step in the proof seems to be justified and correct.

Can someone please explain what is wrong with this proof?

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# Uniqueness of limit by transitive property?

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