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Math Help - Question regarding delta-epsion proof

  1. #1
    Member maxpancho's Avatar
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    Question regarding delta-epsion proof

    Question regarding delta-epsion proof-proof.png

    Why is this sign, that I highlighted in yellow, changes to the equal sign? Sevens just cancel, why would something else have to happen? Also, we are proving that this expression we started with in our proof is less than $\epsilon$ as we show in the subsequent statement and not equal.
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  2. #2
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    Re: Question regarding delta-epsion proof

    The overall inequality you need still holds.

    They are just saying that $7(\epsilon/7)=\epsilon$ which as you note is obvious.

    The < sign on the line above still causes $|(7x-1)-27|<\epsilon$
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    Member maxpancho's Avatar
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    Re: Question regarding delta-epsion proof

    Oh, I think I got it. So they are just explicitly noting that we have this sign <, but the actual quantity after this sign is going to equal to $\epsilon$ hence this equality sign.
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