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Astro021
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I want to see a proof why 0.999999... Is not equal 1 or why is it
Astro021 said:I want to see a proof why 0.999999... Is not equal 1 or why is it
https://www.physicsforums.com/searc...elevance&c[node]=4+73+109+74+228+75+76+78+189PeroK said:There must be dozens of threads on here covering this.
Yes, 0.99... is equal to 1. This is because the ellipsis (...) represents an infinite number of 9's, and when all of these 9's are added together, they equal 1. This can be proven through mathematical equations and proofs.
0.99... is equal to 1 because in the decimal system, there is no number between 0.99... and 1. This means that they are essentially the same number, just represented in a slightly different way. Additionally, as mentioned before, the ellipsis represents an infinite number of 9's, which when added together, equals 1.
This concept has real-world applications in fields such as calculus and number theory. It also has applications in computer science, where the concept of "floating point arithmetic" can cause issues when trying to represent numbers that have infinite decimal representations, such as 0.99...
One example is the following equation: 1/3 = 0.333... If we multiply both sides by 3, we get 3/3 = 0.999... which simplifies to 1 = 0.999... Therefore, 0.999... is equal to 1.
One common misconception is that 0.99... is just an approximation of 1, rather than being exactly equal to 1. However, as explained before, 0.99... and 1 are the same number, just represented in different ways. Another misconception is that this concept only applies to the decimal system, when in fact it can be applied to other number systems as well.