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Related to your comment, not the original post/book:

- On Knuth’s idea (which seems good to me), see http://quomodocumque.wordpress.com/2012/05/29/knuth-big-o-ca... but also the last two comments by David Speyer.

- And see also http://cornellmath.wordpress.com/2007/08/28/non-nonstandard-... and http://texnicalstuff.blogspot.in/2011/05/big-o-notation-for-... that seem to have tried teaching along somewhat similar (but different) lines.

- See https://terrytao.wordpress.com/2022/05/10/partially-specifie... for a further formalization of O notation.

(These links via comments I left to myself at https://shreevatsa.wordpress.com/2014/03/13/big-o-notation-a...)





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