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Dragonfall
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If anyone has any further doubts about 0.999... being equal to 1, please direct your attention to today's http://en.wikipedia.org/wiki/0.999..." .
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Eek! Aargh! Grumble, shriek, not another thread on this!Dragonfall said:If anyone has any further doubts about 0.999... being equal to 1, please direct your attention to today's http://en.wikipedia.org/wiki/0.999..." .
Stevedye56 said:There are only 500 threads about this...
The equality has long been taught in textbooks, and in the last few decades, researchers of mathematics education have studied the reception of this equation among students, who often reject the equality
There are several ways to prove that 0.999 is equal to 1. One way is to use the fact that every real number has a decimal representation. In this case, 0.999 is simply another way of writing the number 1.
While 0.999 and 1 may look different, they are actually just different ways of writing the same number. Just like 1/2 and 0.5 are different representations of the same fraction, 0.999 and 1 are different representations of the same real number.
Some people may have a hard time accepting that 0.999 is equal to 1 because it goes against their intuition. We are used to thinking of 0.999 as almost 1, but in reality, it is exactly 1. Additionally, the concept of infinity can be difficult for our minds to grasp, making it hard to accept that 0.999 is equal to 1.
Yes, there are many real-life examples that demonstrate the equality of 0.999 and 1. One example is the measurement of time. If we divide an hour into 60 minutes, each minute can be represented as 0.016666... hours, which can also be written as 0.999 minutes. This shows that 0.999 and 1 are two ways of representing the same amount of time.
Limits are used in mathematics to describe the behavior of a function as the input approaches a certain value. In the case of 0.999 and 1, we can think of 0.999 as approaching 1 as we add more 9s to the decimal representation. In the limit, 0.999 becomes equal to 1. This demonstrates the equality of the two numbers.