Articles containing proofs | Mathematical paradoxes | Real numbers

In mathematics, 0.999... (also written as 0.9, in repeating decimal notation) denotes the repeating decimal consisting of an unending sequence of 9s after the decimal point. This repeating decimal represents the smallest number no less than every decimal number in the sequence (0.9, 0.99, 0.999, ...); that is, the supremum of this sequence. This number is equal to 1. In other words, "0.999..." is not "almost exactly" or "very, very nearly but not quite" 1 – rather, "0.999..." and "1" represent exactly the same number. There are many ways of showing this equality, from intuitive arguments to mathematically rigorous proofs. The technique used depends on the target audience, background assumptions, historical context, and preferred development of the real numbers, the system within which 0.999... is commonly defined. In other systems, 0.999... can have the same meaning, a different definition, or be undefined. More generally, every nonzero terminating decimal has two equal representations (for example, 8.32 and 8.31999...), which is a property of all positional numeral system representations regardless of base. The utilitarian preference for the terminating decimal representation contributes to the misconception that it is the only representation. For this and other reasons—such as rigorous proofs relying on non-elementary techniques, properties, or disciplines—some people can find the equality sufficiently counterintuitive that they question or reject it. This has been the subject of several studies in mathematics education. (Wikipedia).

A common question, why does 1=0.999... If you want to know more, Wikipedia has a good article on the subject http://en.wikipedia.org/wiki/0.999... I take back the very last thing I said about it being an 'infinitesimal' - that's a 17th century idea that Newton and Leibniz were very keen

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This is my submission to the #megafavnumbers project. My number is 1010010101000011, which is prime in bases 2, 3, 4, 5, 6 and 10. I've open-sourced my code: https://bitbucket.org/Bip901/multibase-primes Clarification: by "ignoring 1" I mean ignoring base 1, since this number cannot be fo

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The Most Controversial Number in Math

0^0 is highly debated in the mathematical community. Why is 0^0 undefined? Does 0^0=0? Does 0^0=1? In this video I'll address the 0^0 meaning and give you a solid 0^0 proof. Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purc

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The One about 0.999… Repeating Equals 1 // Math Minute [#42] [ALGEBRA] [NUMBER THEORY]

There comes a time in every young man or woman's life when they really have to ask themselves: does 0.999… = 1? The answer is yes, and today's Math Minute will hopefully show you a few reasons why. Subscribe: http://bit.ly/SubTimRicchuiti | Enable ALL push notifications 🔔 The equality be

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#MegaFavNumbers - 7,588,043,387,109,376 by Egi

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AQA Mathematical Studies 2A: The Normal Distribution 09a: Finding Z - Tables

Navigate all of my videos at https://sites.google.com/site/tlmaths314/ Like my Facebook Page: https://www.facebook.com/TLMaths-1943955188961592/ to keep updated Follow me on Instagram here: https://www.instagram.com/tlmaths/

From playlist TEACHING Core Maths (AQA Mathematical Studies)

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How is 0.999... = 1? | #Shorts #YouTubeShorts | Don't Memorise

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This video shows three reasons why 0.9999… equals 1.

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From playlist TEACHING Core Maths (AQA Mathematical Studies)

Applied Calculus – Section (3 2)

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Physics - Special Relativity (10 of 43) Relativistic Kenetic Energy

Visit http://ilectureonline.com for more math and science lectures! In this video I will show you how to find the the kinetic energy of a proton traveling at 0.999c (speed of light). Next video in Special Relativity series can be seen at: https://youtu.be/fbUl4CCsGdA

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