an email to point out someone else's error: how to make it politely

0As titled, could you please modify it as possible as you can, 02br
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00or just modify one or two sentence, 02br
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00to make the following email sounds more 01font01b00normal02b02font00 and 01font01b00polite02b02font00? Thanks a lot for your energy! Osee02br
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00I love your book xxx xxx xxx (a mathematical book). 02br
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00Recently I find some minor errors in it (maybe I am wrong), which I would like to discuss with you below.02br
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00Page 18, Exercise 1.3.5(c): I guess sup(cA) should be inf(cA) since A is only bounded above and c<0.02br
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00Page 20, proof of Theorem 1.4.3: Two problems ocurr with the inequalities (3) and (4). 02br
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01b00First,02b00 the well-order property of natural numbers seems to be used to get 01b01i00m02i02b00 to be the smallest natural number greater than 01b01i00na, 02i02b02br
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00but it does not get mentioned before. 02br
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00This might impare the rigorous flavour of this book.02br
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00Second, Since01b01i00 na02i02b00 could be an integer, so these two inequalities kind of do not make sense unless we assume both a and b are real numbers which are not rational.02br
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00Regards, xxx xxx xxx0-