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Tongji University Advanced Mathematics (4th Edition) P46 Case 5 Question 0
Yes, ε is an arbitrarily small number.

But you should note that this ε has been given when proving the problem, that is to say, it is a constant, no matter how small, it will not change in short.

So, when X0 is also small, can you guarantee that the latter is smaller than the former?

That is, if ε is greater than x under the root sign, the whole formula is greater than X.

The key is to note that ε can be arbitrarily small, but once it is taken, it cannot be changed during the whole proof process! ! He became a constant!