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I am looking for Real Analysis book suitable for self study which is similar to the essence of Visual Group theory by Nathan Carter, which is scrupulous and punctilious in explaining concepts via visuals without compromise of rigor. It must be suitable for introductory course. Thanks.

PS I checked other answer to similar question and didnot like the recommendation much, more reference would be useful

ruh
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Confused Simpleton
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    I suspect that the “visual real analysis introductory texts" are the calculus books. – Pedro Apr 10 '20 at 17:56
  • If you want to self-study analysis, take a classic book and sweat on it. I would recommend Walter Rudin's "Principles of mathematical analysis", but there are many other choices. Many other books end up being a watered down version of these classics. – Giuseppe Negro Apr 10 '20 at 18:03
  • This book has lots of pictures and may be what you are looking for. –  Apr 10 '20 at 18:04
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    Rudin and Pugh seems to be advanced books – Confused Simpleton Apr 10 '20 at 18:21
  • Both are considered introductory texts for Real Analysis. If they seem advanced, it is because you don't understand real analysis yet. These are the basics of it. Real analysis is calculus made rigorous, and you cannot do that without laying down the proper foundations. What exactly are real numbers and their properties? What is a limit, and on what does it depend? Why are the extreme and intermediate value theorems true? These are what real analysis is built on. – Paul Sinclair Apr 11 '20 at 01:43
  • @PaulSinclair so how do I lay the foundation – Confused Simpleton Apr 11 '20 at 03:43
  • I suggest that you pick either Rudin or Pugh and start reading. Don't be hasty in forming judgments. –  Apr 11 '20 at 05:28
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    Also, several theorems in real analysis can be associated with a geometry very well, and it is infact a very good exercise for you to draw this parallel. But pictures are a double-edged sword. They are often very useful, there's no doubt about it, but they can also cloud your thinking either by limiting your capacity to think from a more general/abstract perspective, or from inhibiting you to the variety of non-intuitive examples and counter-examples: Cantor sets, countability of various sets, the existence of space-filling curves, continuous-but-nowhere-differentiable curves, etc. – peek-a-boo Apr 11 '20 at 07:47
  • "Understanding Real Analysis" by Stephen Abbott; "Introduction to Real Analysis" by Bartle and Sherbert provide good intuition, along with the necessary rigour for an introductory course in Analysis. – abcd123 Aug 10 '20 at 16:32
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    Does this answer your question? Real Analysis book with pictures and ideas of proofs –  Jul 22 '21 at 08:33

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