Does 0.9999... = 1? NO : Why All Proofs for 0.999...=1 are Wrong. Please Discuss On Social Media

This video explains in detail why all proofs for 0.999...=1 are wrong. It presents both sides of the argument but with a bias towards the position that 0.999... does not equal 1. It points out the problems with the foundations of mathematics that are highlighted by this dispute. Please go ahead and discuss the issues raised in this video on your chosen forums and social media platforms.

Video Guide:

00:00:00 Preamble: Very brief section questioning what it means for mathematics to be logically correct.

00:00:41 Synopsis: Says that this video will question the value of mathematical definitions and rules of logic where these things are just made up instead of having a firm basis in physical reality. As such it will question the validity of limits and abstract axiomatic systems.

00:02:43 Foreword: My experience is that mathematicians are intolerant of opposing viewpoints and I have even been told that I have been banned because my arguments might corrupt young minds (this is similar to creationists banning the teaching of evolution).

00:06:55 Intro: The symbol 0.999... has different meanings and so it is not exclusively reserved to mean 'the limit of the corresponding sequence'. And not even all mathematicians accept the concept of 'real numbers'.

00:10:00 Explains why a non-mathematician might claim it makes no sense to say that unending non-zero terms can be said to 'converge to' a constant value, using 0.999... and the so-called square root of 2 as examples.

00:16:42 This section describes the history of unending sequences in Ancient Greece and includes Zeno's paradox of Achilles and the tortoise.

00:22:37 About geometric series: It seems like the word 'limit' is also called 'sum' to make it sound like an infinite amount of non-zero terms can add up to a constant. It is far from convincing because it relies on definitions. The geometric series is effectively said to equate to a constant 'by definition'. And the basis of equivalence between different geometric series does not seem to be fair.

00:28:07 Problem 1: The first problem with the mathematician’s intuitive explanation which shows no points can exist on the number line between 0.999... and 1 is that we can use the same logic just switched around to argue that points MUST exist between 0.999... and 1.

00:32:04 Problem 2: To say that we can imagine infinitely small points on an infinitely thin number line is far from 'intuitive' and is arguably impossible.

00:33:19 Problem 3: How can all the partial sums 0.9, 0.99, 0.999 and so on exist as static points in static unchanging positions on the number line without there being a last one of these points before 1?

00:35:25 Problem 4: The formal proof version of the intuitive explanation starts with the (invalid) assumption that 0.999... must be a constant.

00:38:11 Problem 5: How can the proof that 0.999... equals a constant be valid regardless of whether or not the starting assumption that it equals a constant is valid or not?

00:38:40 Problem 6: Why it is highly dubious to claim that the division process for 1 divided by 3 yields an infinite result with no remainder part.

00:41:57 Problem 7: Why 1 minus 0.999... yields an unending series, not the constant zero.

00:43:44 Problem 8: Why the shift-and-subtract operation performed in the algebraic proof completely invalidates the so-called proof. This section includes discussion about the Riemann rearrangement theorem.

00:50:04 Problem 9: Why the argument that 1/3 has a finite representation in some bases does not mean that a corresponding representation must exist in base 10.

00:52:02 Problem 10: Why it is highly dubious to argue that the representation of a number is not the number itself, and why set theory doesn't clarify matters.

00:58:42 Problem 11: Why arguments based on methods for supposedly constructing so-called real numbers are just re-packaged versions of previous arguments that we have already found to be invalid.

01:00:10 Problem 12: Why the nested intervals theorem argument is just a re-packaging of the so-called intuitive argument. It also introduces more issues by suggesting that an arbitrarily small interval can exist, and that it can contain exactly one number.

01:01:46 Problem 13: Why the mathematician’s acceptance of arguments that are 'logically valid' make a complete mockery of mathematical logic.

01:04:57 Summary comparison showing the key areas of disagreement

01:06:36 Overview of disagreements concerning some foundational principles of mathematics. This includes why mathematicians appear to like mystery rather than clarity, they prefer usefulness over correctness, they belief mathematical proof is invincible and that it is fine to ban people they label as 'cranks'.

01:16:52 Conclusion: Unless we accept a load of absurd arguments, then 0.999... cannot equal 1. Also mathematics is not a science because it is not based on empirical evidence. It is merely a popularity contest for make-belief theories.

Видео Does 0.9999... = 1? NO : Why All Proofs for 0.999...=1 are Wrong. Please Discuss On Social Media канала Karma Peny