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The simplest argument I can think of is to ask yourself: "Are there any numbers between 0.999... and 1?" If not then it's logical to conclude they wind up at
by aguaviva 2y ago
The simplest argument I can think of is to ask yourself: "Are there any numbers between 0.999... and 1?"
If not then it's logical to conclude they wind up at the same "place", that is, the same number. Or equivalently: it can't have any other value besides 1.
If you care about such things, then you're a mathematician.
- ForOldHack 2y agoIt is a limit. A very powerful tool. You can choose any arbitrary finite number in the sequence, and I can find a number greater. So the value of 1 exists, and its a continuous function, so therefore the limit exists. I do care about such things, and yes, a degree in math for me was just slogging through every math course the college had, with a long string of high grades, and honor roll achievements.
- floxy 2y ago1/6 = 0.166666...6 1/6 = 0.166666...6 1/6 = 0.166666...6 1/6 = 0.166666...6 1/6 = 0.166666...6 + 1/6 = 0.166666...6 ---------------------- = 0.999999...6 ...so that 6 times 1/6 is zero point 9 repeating, with a 6 on the end ;-)