Arguably all of them, Jesus permitting.
I don’t wish to start another thread in IMHO, but isn’t it more probable that 7s is trolling rather than being batshit crazy?
Of course, he could be both.
<Prince Humperdinck>I think everybody could be a troll. That’s why I’m still alive </Prince Humperdinck>
I kind of doubt it. He’s either an incredibly dedicated troll or just another in a long line of people who are smart/educated enough to be dangerous but not smart/educated enough to know how little they know.
They’re common enough that trollery isn’t even the most likely possibility.
You admit you don’t understand the matter, but you insist on maintaining an opinion that you can’t support and has been declared and proved incorrect by experts? And not just shrugging and saying you don’t know, but stubbornly insisting that you’re right?
Nice
Others have discussed the fact it isn’t just a debate against one person, so I’ll expand on this.
It isn’t a fine point. It’s a great honking fundamental point which is central to a huge field of mathematics called Analysis, which is usually introduced to students in the form of the differential and integral calculus of real-valued functions of one variable. Analysis is concerned with the concepts of closeness, limits, and smoothness, and so one of the central topics is “When do infinite series have a value, and what are those values?”
Therefore, the idea that infinite series can have finite values, an example of which is the fact 0.999… == 1, cuts right to the heart of what Analysis even means, which means it’s a topic that’s taught early in the introductory courses and is returned to repeatedly through the later ones, in different forms. Since a lot of us have taken at least two semesters’ (one school year’s) worth of introductory differential and integral calculus, it’s a topic a lot of us are qualified to talk about, and so we do. Over and over again. To new people who come by and, for some reason or another, cannot accept that real numbers are defined objects with well-understood behavior, which can be correct even if some find it counterintuitive.
I will agree with you that 1/3 + 1/3 + 1/3 = 3/3, which = 1.
I know this interpretation is technically accurate, but people can clearly still conceive of said number. So, rather than argue such a number can’t exist, I act as if it does. If a number such as 0.000…01 existed, with an infinite number of 0s before the 1, there would be no number between it and 0.
You try to cut it half, for instance. You get 0.000…005, which is the same thing as 0.000…05, which would be 5 times greater than 0.000…01. No matter what mathematical operation you attempt, you cannot get a number smaller than 0.000…01. (Smaller in this case meaning having a lower absolute value.)
The thing is, the real numbers are continuous, meaning there’s no smallest unit. You can always make a smaller one. This means that, if there is no smaller number you can make, the only possibility is that the numbers are equivalent.
You can think of it this way. You are adding one digit to an infinite number of digits. And what is infinity + 1? It’s still infinity. 0.000…01 = 0.000…00 = 0.
Well, no, not really. They can imagine something like it, but, when pressed, they cannot define it.
It isn’t even as blatant as “I can conceive of a unicorn.” At least I can define a unicorn.
It’s more like “I can conceive a prime number greater than two.” And, yes, I actually can. My brain is perfectly willing to do this. But my brain is wrong in this. My “conception” is actually self-contradictory.
It ain’t necessarily so. We can build a syntax which distinguishes between these strings and treats them as referring to different numbers.
A winning argument among ten year-olds.
NOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO. :eek:
There must be something about this topic… something that makes these incessant cycles an inevitable low-energy state. There’s a force at work here that is faster-acting and more inexorable than Godwin’s Law. I’m horrified but I can’t look away!
What’s missed is the concept of what is infinitely small.
0.999… is infinitely close to 1, which means it is 1. A better example is an infinitely short period of time, dt, which occurs in zero seconds. It is instantaneous.
But FOURTEEN fucking years?
Personally, I’m okay with 0.999… = 1 and …999 = ∞
And if I’m wrong, may we all be horribly crushed from above somehow.
…an even prime greater than two?
Because I can easily conceive of a prime number greater than two without any contradiction. Almost every prime is greater than two.
Grin! I can also conceive of actually typing what I meant to say. How’s that for a far stretch?
Yes… Thank you… I can conceive of an even prime number greater than two, even though such a thing cannot exist.
I can also look at weird optical illusions, like the “blivet” optical illusion, and conceive of these objects as real. The brain is capable of really weird things.
To paraphrase the Red Queen, I can conceive of six impossible things before breakfast.
This isn’t missed, it’s irrelevant. Infinitesimals don’t exist in the reals, and anyone who tries to argue against that point has already proven they are in no way competent to argue against that point.
That’s besides the point, but if you like: 0.999… + i = 1 + i.
has the main thread ran out of places such that we need another thread on the exact same thing? why not contribute to it instead and see if it can go on indefinitely?
I was thinking we need to open a thread in Great Debates as well, the subject material deserves three separate threads at least.