I have just finished some analysis which seems to rely on the property that if $ 0 < x \leq a$ then, as a tends to zero, x will tend to a. Is this a valid property? I was wondering if there might a formal proof of the property?
Thanks in advance
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Sign up to join this communityI have just finished some analysis which seems to rely on the property that if $ 0 < x \leq a$ then, as a tends to zero, x will tend to a. Is this a valid property? I was wondering if there might a formal proof of the property?
Thanks in advance
It is the comparison theorem: if $\alpha \leq \beta \leq \gamma$ and $\lim \alpha = \lim \gamma=\ell$, then also $\lim \beta =\ell$.