What is Digg?235 Comments
- jamesallen74, on 10/11/2007, -11/+81So that's how Bush got elected in 2000. Damn!
- phatphil, on 10/11/2007, -13/+80Step 3 is not equal to step 2, i/1 ≠ 1/i.
- Syric, on 10/11/2007, -1/+56You can't "divide out (a-b)", because if a = b, then (a-b) = 0. And you can't divide by zero. Pretty obvious if you ask me.
- jamesallen74, on 10/11/2007, -5/+38the math geeks are coming out of their caves now
- BassMastr, on 10/11/2007, -2/+34You lost me at 1=...
- BLyn, on 10/11/2007, -2/+34Is that division of (a-b) not defined since a=b? Doesn't make complete sense but it was the best reason i could come up with.
- Grambo, on 10/11/2007, -2/+25Dividing by (a-b) is division by 0.
- borninda818, on 10/11/2007, -1/+21I like chicken
- sid0, on 10/11/2007, -3/+23Why is phatphil being dugg down? He's absolutely right. You simply CANNOT separate square roots into numerator and denominator when dealing with negative numbers inside them! Haven't you ever learnt any math(s)? *sigh* kids these days.
- slipgrid, on 10/11/2007, -2/+20First of all, ∞ is not a set of numbers, but one and only one number. Second of all, ∞ != -∞.
- jspayne, on 11/10/2007, -0/+17It makes complete sense because a-b is 0 - division by zero is undefined
- kirkness, on 10/11/2007, -1/+15... what color were the train conductors shoes?
- jmpeagle, on 10/11/2007, -1/+14but it does not equal a fraction of integers. The c has a multiple of pi in it. You could say any number is a fraction by putting a multiple of it in the numerator or simply a one in the denominator
- derlavai, on 10/11/2007, -0/+13god. people please read the answer before declaring yourselves god's of complex numbers. this hardly touches the topic.
- Urusai, on 10/11/2007, -0/+12Never trust a division. Division is not closed, unlike your other typical operators. Exponentiation is a minefield, too. In fact, just screw it and major in philosophy.
- smackhero, on 10/11/2007, -1/+13right,
|sqrt(1/-1)| = |sqrt(-1/1)|, not sqrt(1/-1)=sqrt(-1/1).
so it should have been ±sqrt(1/-1) = ±sqrt(-1/1) - webcure, on 10/11/2007, -9/+21I love this kind of stuff. I don't understand it much, but I love it anyway.
- Uranium118, on 10/11/2007, -0/+10"a = b : given"
so
a - b = 0 - jmpeagle, on 10/11/2007, -2/+12true but your logic is flawed, just because a number cannot be made by an equivalent fraction just means it is irrational not necessarily non-existant. There is no fraction equivalent to pi.
- SqueakyMouse, on 10/11/2007, -0/+10The problem is that e^ix is not an injective function on that domain.
http://mathworld.wolfram.com/Injection.html
It may become clearer if you use the identity e^(ix)=cos(x)+isin(x). There are many values of x satisfying this due to periodicity, so you can't invert it to a unique real number. - robdiggity, on 10/11/2007, -1/+10My Pentium (tm) says so!
- SpeedyG, on 10/11/2007, -0/+9And of course, if anybody kept reading, they'd notice that the problem is on a math teaching website, the url contains the phrase "falseProofs", and the very end of the proof says to select the incorrect line of the proof. But of course, yet another misleading article description.
- nyx210, on 10/11/2007, -1/+9No. C++ == C.
++C > C. - kodek, on 11/10/2007, -1/+9Oh God, not the .999... = 1 thing again...
- smackhero, on 10/11/2007, -0/+8compromise? math is not politics or diplomacy. there is no such thing as compromise in math. nor is it a virtue. math should be about absolutes. otherwise it is useless.
- DeskFlyer, on 10/11/2007, -5/+13I tried reading all of that but my head exploded halfway through... :(
- Bitruder, on 10/11/2007, -4/+11The problem is that 2*p*i is actually 0. Think of a circle... if you go around 0 radians, you are where you started. If you go around 2pi radians, you are where you started. :)
- kingkilr, on 10/11/2007, -0/+7C++ > C , by 1
- m0oSe, on 10/11/2007, -5/+12.999~ = 1
proof:
lim(m --> ∞) sum(n = 1)^m (9)/(10^n) = 1
0.9999... = 1
Thus x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1 - smackhero, on 10/11/2007, -1/+8you're an idiot.
- sid0, on 10/11/2007, -2/+9"You might as well say .499... = .5, 0.0999.... = .1, and .333999... = .3334."
And you would be perfectly correct! Of course .999... is a number, it is simply equal to 1.
Want to know how to produce it from a "fraction"? 1/3=.333... as you mentioned, then multiply both sides by 3. - Syric, on 10/11/2007, -2/+9How about this:
Notation: p = pi = 3.1415... (since I don't know how to type pi). i = (-1)^(1/2), ie., the square root of negative one
e^(p*i) = -1 (given, and true; check it out on a calculator)
[e^(p*i)]^2 = (-1)^2 (square both sides)
e^(2*p*i) = 1 (simplify)
ln(e^(2*p*i) = ln(1) (take the natural log of both sides)
2*p*i = 0 (simplify)
From this, we conclude that either 2 = 0, p = 0, or i = 0 .
From which we can state that (any number) = (any other number) as a corollary.
Obviously that's not true. What's the fallacy?
Edit: I'm not trying to be a smartass; I actually don't know what the fallacy is. It's been stumping me ever since I came up with it. - MasherSCF, on 10/11/2007, -1/+8You can't divide by zero. There are actually about 20 proofs that 1=0 from different branches of math. Each is wrong in it's own way. Some are quite perplexing. Some are beyond the understanding of most mortals.
- robdiggity, on 10/11/2007, -1/+7My cat's breath smells like cat food.
- HPCELarry, on 10/11/2007, -1/+7well you see thats actually true. This article however, make no sense. If 1=2 then numbers don't matter at all. It destroys the entire deffinition and purpose of numbers to have different ones equal each other.
- adamlazz, on 10/11/2007, -1/+7Think of a number. Now multiply it by 9. Now divide it by 9. Is it the same number as when you started?
Place your tips in my magician hat. - TheCaterpillar, on 10/11/2007, -0/+6.9 repeating IS equal to 1, soo good job!
- UnConeD, on 10/11/2007, -0/+6The logarithm of a complex number can have an arbitrary shift of a multiple of 2πi. So your 4th line should be:
ln(e^(2πi)) = ln(1) + k2πi (where k ∈ ℤ)
and there is no contradiction at the end. Using your faulty logic, you could use "(-5)^2 = 5^2" to 'prove' that -5 = 5. - MasherSCF, on 10/11/2007, -0/+6You're exactly right. The trouble is above that in step 2 to 3. Notice, sqrt(-1/1)=sqrt(1/-1) => i = i. There's no problem there. The trouble is that once a minus is under the radical, the normal rules of manipulating radicals no longer apply. Observe, 1/i = (1/i)(i/i) = i/(i^2) = i/-1 = -i. Therefore, step 3 is wrong.
- Wildren, on 10/11/2007, -3/+8thee proof is flawed, it's actually a game. Buried as inaccurate title.
- inactive, on 10/11/2007, -0/+5SqueakyMouse is correct. You have to be careful with various branches of the logarithm when working with complex numbers.
- johndi, on 11/10/2007, -10/+15Fractions are messy. The number .999... is a made up number, it doesn't exist. It's not like 1/3 = .333... where you can get to it directly through division. You have to add other repeating decimals to create it. However you can't do that without truncating them, or just assuming that it would work out.
You might as well say .499... = .5, 0.0999.... = .1, and .333999... = .3334. I can create fantasy numbers all day that aren't naturally repeating decimals. - sid0, on 10/11/2007, -0/+5I dislike the term "imaginary" because it seems to imply numbers that don't exist, when they actually do exist. "Proof" of their existence is any basic LCR circuit, where, beyond the simplest cases, complex numbers have to be used to find effective impedances.
- robdiggity, on 10/11/2007, -0/+5No, sorry, "the rules of mathematics" (or whatever the ***** you are talking about) do not state anything of the sort. If a=b, then a-b = 0. Done. Go back to algebra class.
The rules of mathematics! Seriously, thanks for cracking me up today :) - psygnisfive, on 10/11/2007, -0/+5Actually the error is in the step before it.
- rmacnguyen, on 10/11/2007, -0/+5...So you're saying you can't divide by negative numbers...? I suggest you type 1/-1 into your calculator and see what it gives you. If I were to take a guess, I think it'd be -1, not undefined.
- batoari, on 10/11/2007, -0/+5Add 3 to both sides and divide by 2. In fact, given that it's possible to prove that all numbers are equal.
Let's say you want to equate n to m, first subtract 1 from both sides of 1=2 to get 0=1. Then multiply both sides by m-n to get 0=m-n. Finally, add n to both sides and you have n=m.
This is why if 1=2 all of mathematics collapses. - msmearcheck, on 10/11/2007, -0/+5i thought this would be something creative
- sid0, on 10/11/2007, -1/+5... says a person who writes "retarted".
- maffematician, on 10/11/2007, -0/+4it was my username that gave me away, wasn't it?
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