The conclusion can directly tell you that the period of 0.99999 is equal to 1, and the proof process is very simple. Let the period of 0.999999 be equal to X, then 10 multiplied by the period of 0.999999 is equal to 9.99999, that is, 10x=9.99999, which is not repeated. The specific proof is as follows:
Here we come to the conclusion that the period of 0.99999 is equal to 1. Of course, the more professional statement is that the period of 0.9999 is infinitely close to 1, or the difference between the periods of 0.99999 and 1 is infinitely close to 0.
But don't panic, it's not over yet, because in mathematics, besides the equal sign "=", there is a stronger equal sign called the constant equal sign "80 1", which has three small horizontal lines. Although we have proved that the period of 0.99999 is equal to 1, the period of 0.999999 is not always equal to 1. What does this mean? In some cases, the difference between the period of 0.9999 and 1 is infinitely close to 0, but this little difference will lead to completely different results. Please see the following proof:
There is a little math threshold here. Let the 0.99999 cycle and 1 do the power operation of 10 respectively, and any power of 1 is 1, and 0.9999 does the power operation of 10. When n tends to infinity, the answer is the reciprocal of e, where e is the natural logarithm and e ≈ 2.7 1 828128459045 is1.
So the conclusion is that the period of 0.99999 is equal to 1, but not necessarily equal to 1.
Ok, that's all for today's introduction. Please automatically ignore my typo handwriting. Are you impressed by magical mathematics? The more I do popular science, the more I really respect math. What other puzzles do you have about mathematics? Please leave a message in the comments section. If it is within my mathematical ability, I will answer them.