Who knows? By the year 3000, they might be commonplace. To future readers of this post: if you’re going to have public suicide machines, kill two birds with one stone by installing them in poll booths, make elections mantatory, and allow free suicides. I wonder what will happen?
Kozmik, I know you’re being deep and all, but could you please lay out what you’tr trying to say in something close to plain English? Thanks.
Alright, I’m going back to the basics! So here we go. You can put in any number for x and can solve it, except for one certain number…
x is not the same as 3 or 153 or 155 or 4761 or 186457 or any other number. Everybody got that? Great. Now on to the problem.
x – x = x / x – 1
So far Lemur, Voyager, ultrafilter, SentientMeat, and Magetout have solved this equation. But you know what? That doesn’t matter. Why? Because you *can’t * write out the proof!
To summarize -
You can put any number for x and solve it, except for a certain number.
This number isn’t like any other number.
You can solve x – x = x / x – 1 but you can’t write out the proof
Tell us the number, or admit that you’re sniffing glue and staring at a freshman algebra textbook.
In case you didn’t notice, I already gave away the number.
Kozmik, I could disagree with any one of your twelve principles, if I could be arsed. And yes, x/x=1 is undefined for x=0, and I could explain that to you also if I could be arsed.
But I can’t. Goodbye.
Wait. Please accept my apologies. I don’t care if you disagree about the tweleve principles. They are just a guide. It just shows where I’m coming from. I believe in the the Platonic ideas. Somethings I don’t know what to believe.
I was excited that I might have found something profound to think about. I got inspired by the Monkey Shakesphere problem. I thought how we all started out learning that 3 - 3 = 0. Heck, I even remembered the flashed cards. But there is one very special number…ok let me explain, I don’t want to bias the results. I want you to find it inductively.
It would be easy to say, I believe that I found a remarkable proof.
I’m trying to get the words out. There are some thing in math that I can’t even fathom. Numbers are so basic, so pure and they.
My inspiration for this thread was that I can never look at an equation with an infinite or indeterminite value. But it’s about knowing the answer. I can never look at this infinite string of numbers but I know at the other side there is an answer.
Please look,
3 - 3 = 0 This changes nothing
∞ - ∞ = 0 This changes everything
An infinite number, though not infinity.
An infinite number that we can never see in full. Yet we know the answer.
No, you have made this up - every trained mathematician would wrinkle their nose in disgust at this equation. That sideways “8” symbol is not a number, but a representation of a process. You simply cannot manipulate it like other number symbols.
In fact, it’s entirely possible for an infinite set minus another infinite set to equal three.
I suppose it’s possible for the difference to be any number you like; or for the sum of an infinite set to be twice the sum of the other (or infinitely greater than the other)… All bets are off.
Kozmik, I understand your awe about numbers, whose nature and ultimate foundations have puzzled philosophers and mathematicians for millennia. However, I don’t think you’ll be able to get much help from the SDMB or anyone else until you can frame your points more coherently. Try reading this book and see if it helps.
My point exactly. Or they could be identical. You just can’t say.
I don’t follow this at all. How are all of your numerical examples of 0.25 representations of x/x?
The only number I can see that doesn’t satisfy x - x = x/x = 0 is zero itself. And that is only because division by zero isn’t an allowed operation in mathematics. There are many equations that zero will not satisfy.
Just off the top of my head:
x*n + 3 = n has no solution for n = 0 but works just fine for all other n.
Oh I see. Yes, it is very cool that in algebra you manipulate variables, not numbers. But the rest of us have gotten over this decades ago. I don’t see anything deeper than this revelation here.
BTW, when you solve two equations in two unknowns, do you try every possibility, or do you use the standard techniques to find the answer in a reasonable amount of time?
I missed this one. It is not true, since x must be consistent in the equation, and the numerator is not equal to the denominator in any of the variations of 1/4. As for going on forever, isn’t that taught in elementary school these days? And it is not clear that 1/4 is first - -1/-4, -2/-8 are also members of the sequence.
4 - 4 = 0
∞ - ∞ = 0
4 is a finite number
∞ represents an infinite number (infinite because the number can never be written out; the digits never end)
I know that 4 - 4 = 0,
therefore, I know that ∞ - ∞ = 0
I imput 4 - 4 into the a supercomputer and the output is 0
I imput ∞ - ∞ into the a supercomputer and there will never be an output…but I know the answer is 0
This is the error in your argument. ∞ on its own is a meaningless symbol, and in any context where it does have meaning, it doesn’t represent a single value. If you want a more authoritative source, check Walter Rudin’s Principles of Mathematical Analysis (don’t remember the page number off the top of my head, but I can check when I get home).
I think you still don’t understand what ∞ actually represents. It’s not a number. It’s not x. It does not represent “an infinitely large number” because there is no such thing. You can manipulate ∞ in specific ways, but it does not hold up to algebra, I’m afraid.
Actully old CDC machines, which were ones complement, had a -0 which I believe was sometimes used to represent infinity. Subtracting -0 from -0 did not cause it to run forever - it probably caused an arithmetic check. So you’re wrong even there, and as others have said, you have a simplistic view of infinity.
Example:
There are an infinite number of integers, right?
There are an infinite number of even integers, right?
Now, subtract the even integers from the integers, and count the quantity of the result.
By you’re argument, you should get 0. Actually, you get all the odd numbers, the number of which is infinity also. So ∞ - ∞ = ∞, and you just failed math. 
.25407909145135711136941091193932519107602082520261879853188770584972591677813149699009019211697173727847684726860849003377024242916513005005168323364350389517029893922334517220138128069650117844087451960121228599371623130171144484640903890644954440061986907548516026327505298349187407866808818338510228334508504860825039302133219715518430635455007668282949304137765527939751754613953984683393638304746119966538581538420568533862186725233402830871123282789212507712629463229563989898935821167456270102183564622013496715188190973038119800497340723961036854066431939509790190699639552453005450580685501956730229219139339185680344903982059551002263535361920419947455385938102343955449597783779023742161727111723643435439478221818528624085140066604433258885698670543154706965747458550332323342107301545940516553790686627333799585115625784322988273723198987571415957811196358330059408730681216028764962867446047746491599505497374256269010490377819868359381465741268049256487985561453723478673303904688383436346553794986419270563872931748723320837601123029911367938627089438799…
This is an infinite number. Defintion: it never ends; it can never be written out.
BUT if I subtract it by itself, I know the answer is 0