I know many of you will know this already, but for those of you who don't, this will destroy the foundation of mathematics as you know it. Yes, that's probably exaggerating
Let's say a = b. Both are non-zero integers.
a = b
Let's multiply both sides by a.
a^2 = ab
Take away b^2 from them.
a^2 - b^2 = ab - b^2
Factorise it...
(a - b)(a + b) = b (a - b)
Cancel the (a - b)s...
(a + b) = b
a + b = b
Remember that a = b and substitute...
b + b = b
Simplify it
2b = b
And, finally, divide by b.
2 = 1
Yes, you heard me right.
2 = 1.
As the title implies theres a fallacy there sumwhere. When you say 2b = b there's only one number that can fill it, 0. Just because 2b = b doesn't mean you can replace b with anything you want. I'm sure you've done "Find x" problems before.
Quote from: AHadley on November 19, 2009, 06:52:28 PM
2b = b
And, finally, divide by b.
2 = 1
INCORRECT! B is 0. Dividing both sides by B is dividing by zero. The fabric of space time breaks down when you divide by zero. Hence, 2=1
QuoteThe fabric of space time breaks down when you divide by zero.
The fabric of space time is 0, sort of.
Mathematics can be used to model reality, but reality does not do mathematics, maths can be wrong, but reality cannot.
It's called a mathematic fallacy because it is a flaw in mathematics. So MTS is exactly correct.
The flaw is that any pair of non-zero numbers never comes out as the correct answer, although it is assumed by the equation that both A and B are non-zero. I'd better edit that in.
It is at this point that algebra and actual numbers fail to match up. That is why this works as it does. I would dig up the fallacies that prove that 0 = 1 and that all numbers are equal to each other, but they are a little beyond my understanding here at AS level.
There is another one, though.
1/3 = 0.3`
0.3` + 0.3` = 0.6`
0.6` + 0.3` = 0.9`
What is three thirds?
Actually (a-b) is zero. When you "Cancel the (a - b)s...", that's when you're dividing by zero.
you could find the first ignored flaw by looking at the third step.
if a = b
then a^2 - b^2 = 0
and on the other side of the equation, ab - b^2 = 0
therefore => 0 = 0
That's a flaw with the mathematics though, not with the working out. If something is done to one side and the other then the values are affected in the same way and they change to the same thing - or that's the theory anyways.
There is no flaw, it is just above your understanding.
0.33333' + 0.66666' is not 0.99999'. Because both decimals extend into infinity, to claim they sum in that way suggests they do NOT continue into infinity. In reality 0.33333' + 0.66666' = 1.0
I can look for an inductive proof of such if you so require.
I did point out that I'm only AS level (just starting on differentiation and integration) so most areas of mathematics are no doubt beyond me, so please do explain in terms I can understand if you can overcome the fallacy.
I do however believe that mathematics is in no way perfect. It is, as MTS said, only a model.
Math is perfect in our current physics set. The very basics of math, by that I mean Algebra, Geometry, and Calculus always hold true.
I am not even a math major. I hate proofs with a passion. But trust me, the math works perfectly.
Remember that math is the purest science. (http://xkcd.com/435/)
Quote from: AHadley on November 19, 2009, 09:37:17 PM
That's a flaw with the mathematics though, not with the working out. If something is done to one side and the other then the values are affected in the same way and they change to the same thing - or that's the theory anyways.
The flaw has everything to do with the 'working it out' part.
By definition, a is equal to b. This fact is conveniently forgotten in the "Cancel the (a - b)s..." step.
Since a is equal to b, then a minus b is zero. period.
Therefore cancelling (a-b), also known as dividing by (a-b), is an illegal operation. A division by zero.
I agree with you on the "both sides are affected" part. In this case however, both sides equate to undefined. Therefore undefined still equals undefined.
Wikipedia may be able to explain it better that i do. (http://en.wikipedia.org/wiki/2%3D1#Proof_that_2_.3D_1)
Division by zero is not technically illegal in higher math, it just means "all solutions reach infinity" or some such nonsense.
.99999...... is exactly 1. Let me prove it...
x = .999999999...
Multiply both sides by 10
10x = 9.999999999...
Because x = .99999999..., let's subtract it (x) from both sides
9x = 9
Divide both sides by 9
x = 1 = .999999...
EDIT:
ScarleTomato is exactly correct:
a = b
Let's give them number values:
5 = 5
So when you subtract a from b:
(a - b) = (5 - 5)
What's (5 - 5)?
What's (a - b)?
When the denominator of an equation =0, graphically you end up with a function where somewhere it has a vertical slope. If the slope is vertical, it has an infinite number of points "stacked up" and it does not pass the vertical line test to describe a function. In other words, when f(0) = anything divided by zero (n/0), a vertical asymptote is created where the graph doesn't actually exist at all. The canceling (a - b) from both sides step is impossible.
Here is your first post, with 5's instead of variables:
Let's say 5 = 5. Both are non-zero integers.
5 = 5
Let's multiply both sides by 5.
5^2 = 5^2
Take away 5^2 from them.
(5^2) - (5^2) = ((5^2) - (25))
Factorise it...
(5+5)(0) = 5(0)
(This should be the solution)
Cancel the (0)s...
((5+5)(0))/0 = (5(0))/0
(dividing by 0 makes this statement incorrect, you can't actually do it, so the rest is void:)
5 + 5 = 5
Remember that 5 = 5 and substitute...
5 + 5 = 5
Simplify it
2(5) = 5
And, finally, divide by 5.
2 = 1
QuoteRemember that math is the purest science.
It is also pure fiction. It exists only in the minds of the beings the Universe has seen fit to create for itself. It is not real and it does not even represent reality in any meaningful way.
If you divide 1 atom by 2...you have a great deal of trouble adding it together again.
Quote from: Feared_1 on November 19, 2009, 10:08:19 PM
.99999...... is exactly 1. Let me prove it...
x = .999999999...
Multiply both sides by 10
10x = 9.999999999...
Because x = .99999999..., let's subtract it (x) from both sides
9x = 9
Divide both sides by 9
x = 1 = .999999...
That's some clever stuff. I don't have a thing for working out equations of my own unfortunately :lol:
I shall have to point that out to my maths teacher :-d
Math is not fiction. Math is perfect and applies itself in every aspect of life.
Addition does not undo division. If you divide 1 atom by 2, you have to multiply to get 1 back.
I'm switched over to Math Education major a while back, so I've developed a love for it.
EDIT: By the way, I edited my first post to give more information.
Thats what they thought 300 years ago, but we advanced from there.
Math is the perfect language, the ultimate expression of reality, the purest music in the universe.
We speak it with a terrible lisp, though...
We are blinded, and have but the dimmest glimpse of true reality...
We are tone deaf and can only imagine we understand how pure and beautiful the music of the spheres truly is...
Our understanding of the universe, especially the mathematics of it, is crude at best. We're just infants looking out of our cribs at the wonder that is reality.
The true shame is that we think we know it all. We have such confidence in our world view, and of course anything or anyone that contradicts it is heretical.
It's always been this way. Right now there are those among us rising to defend our paltry knowledge... but anyone who's studied history will see that every year something new is learned, and something thought to be unshakeable truth is shaken to bits...
-Av-
Clearly you have not understood what I am saying.
QuoteIf you divide 1 atom by 2, you have to multiply to get 1 back.
So multiplying the spectrum of radiations and energy's produced by dividing an atom makes another atom?, its not that simple.
Maths looks perfect when expressed as itself. Reality is allot more messy, things explode if you add them together to hard or turn into something else entirely when you divide them. Ultimately math exists only in our heads, calculations are just graphite on wood pulp, or photons hitting a retina. The idea is perfect and very very useful to anything capable of using it, but it is, like all of our thoughts, just another story we tell ourselves. A magnificent Non-thing, powerful but as fragile as we are ourselves and utterly irrelevant to 99.999999' % of the universe.
Quote from: Avatar on November 19, 2009, 11:59:09 PM
Math is the perfect language, the ultimate expression of reality, the purest music in the universe.
We speak it with a terrible lisp, though...
We are blinded, and have but the dimmest glimpse of true reality...
We are tone deaf and can only imagine we understand how pure and beautiful the music of the spheres truly is...
Our understanding of the universe, especially the mathematics of it, is crude at best. We're just infants looking out of our cribs at the wonder that is reality.
The true shame is that we think we know it all. We have such confidence in our world view, and of course anything or anyone that contradicts it is heretical.
It's always been this way. Right now there are those among us rising to defend our paltry knowledge... but anyone who's studied history will see that every year something new is learned, and something thought to be unshakeable truth is shaken to bits...
-Av-
..and that's the beauty of it all. :-)
"This, too, shall pass."
Very well put, Av. :thumbsup:
I don't think that .9' is exactly 1, just that their difference is less than infinitessimly small.
That's a quantity that language expresses just fine, but math doesn't.
If a baseball bat that's missing one atom hits you in your face, does it still hurt?
Noooo......... :-D
Depends on which atom was missing.
Quote from: mrtwosheds on November 20, 2009, 12:08:16 AM
Clearly you have not understood what I am saying. So multiplying the spectrum of radiations and energy's produced by dividing an atom makes another atom?, its not that simple.
Maths looks perfect when expressed as itself. Reality is allot more messy, things explode if you add them together to hard or turn into something else entirely when you divide them. Ultimately math exists only in our heads, calculations are just graphite on wood pulp, or photons hitting a retina. The idea is perfect and very very useful to anything capable of using it, but it is, like all of our thoughts, just another story we tell ourselves. A magnificent Non-thing, powerful but as fragile as we are ourselves and utterly irrelevant to 99.999999' % of the universe.
I think this is funny because you are SO wrong. Math is EVERYTHING. I can't tell you how to apply it, but I can tell you that it can be applied. Just because you don't know how to apply it doesn't mean its irrelevant. Avatar has it right.
EDIT:
Yes, .999... (repeating FOREVER) is exactly 1.
1/3 = .333... (repeating forever)
Look at the "multiply by 10" rule I have up there somewhere.
Is math love?
Yes, I love math :)
Quote from: sabrebattletank on November 20, 2009, 01:11:46 AM
I don't think that .9' is exactly 1, just that their difference is less than infinitessimly small.
That's a quantity that language expresses just fine, but math doesn't.
.9' is not 1
.3' + .6' is not .9'
Quote from: Nielk1 on November 20, 2009, 05:20:06 AM
.9' is not 1
.3' + .6' is not .9'
Great thing about math... if you're going to say anything about it, you have to prove it.
Avatar got it right on the head. Our science is imperfect because we are imperfect.
QuoteI think this is funny because you are SO wrong. Math is EVERYTHING.
What was wrong?
Maths could possibly be used to describe everything, given infinite time and capacity to calculate it.
Reality has that by default, reality is not just mathematics incarnate. Mathematics is a human language.
If you want maths to be everything then you are going to have to start expressing your equations in matter, energy and nothing.
Quote from: Clavin12 on November 20, 2009, 02:40:00 PM
That's not what I asked.
I was joking because your sentence was grammatically incorrect for the context you wanted.
"Is math love?" isn't the same as "Is love math?"
The answer you wanted: It could be if you wanted it to be. Do I need to give examples or can you figure it out yourself?
MTS, I see where you're coming from. Example: The planets don't "use" math to orbit the sun, but that orbit can be defined using math and a pattern can be found pertaining to the other planets to make a "law." That "law" (http://en.wikipedia.org/wiki/Orbit_equation) applies to all planets, even ones that have not been discovered. In fact, it applies to all OBJECTS. It perfectly describes what it needs to. The catch is people not being able to use the equation correctly.
If you don't want "infinite time and space", then you need to add values and variables to give it a specific limit. That's much more complicated, but perfectly possible. Using the example from before: A planet is orbiting the sun as defined by an unnamed orbit equation. A massive meteor strikes the planet and strongly disrupts the orbit of the planet. You can't use the equation anymore to define the orbit because it doesn't apply anymore. You would need to add more variables or values in order to get a mathematical balance again. The issue is that (as Avatar stated), people are not perfect and could easily come up with the wrong equation to describe the new orbit. It may work in that one situation, but in reality it doesn't apply to all.
Quote from: ScarleTomato on November 20, 2009, 05:23:27 AM
Great thing about math... if you're going to say anything about it, you have to prove it.
Quote from: Feared_1.99999...... is exactly 1. Let me prove it...
x = .999999999...
Multiply both sides by 10
10x = 9.999999999...
Because x = .99999999..., let's subtract it (x) from both sides
9x = 9
Divide both sides by 9
x = 1 = .999999...
I didn't say that. He said math is everything and so I asked if math was love. I'm not going to ask is love math because it wouldn't fit the context. Math is not love nor is love math.
Quote from: Nielk1 on November 19, 2009, 08:21:53 PM
INCORRECT! B is 0. Dividing both sides by B is dividing by zero. The fabric of space time breaks down when you divide by zero. Hence, 2=1
Complex Numbers.
Quote from: AHadley on November 19, 2009, 09:10:55 PM
There is another one, though.
1/3 = 0.3`
0.3` + 0.3` = 0.6`
0.6` + 0.3` = 0.9`
What is three thirds?
Only like this if you use Floor rounding. If you use normal or (for some reason) cieling rounding, 2/3 = 0.67 (or 0.7, since you were going to tenths).
0.67 + 0.33 = 1
Quote from: ScarleTomato on November 20, 2009, 05:23:27 AM
Quote from: Nielk1 on November 20, 2009, 05:20:06 AM
.9' is not 1
.3' + .6' is not .9'
Great thing about math... if you're going to say anything about it, you have to prove it.
Shall I do induction on the length of the infinite decimal? That is how they create 100% will happen indisputable proof for math facts.
Quote from: Clavin12 on November 20, 2009, 03:20:42 PM
I didn't say that. He said math is everything and so I asked if math was love. I'm not going to ask is love math because it wouldn't fit the context. Math is not love nor is love math.
How about this:
L = f(L)
f(L) is the dependent variable (H)
Let H be a function of L...Where L is love and H is happiness. Depending on each different person (i.e, throwing in different values and variables), how happy that person is depends on his/her relationships. If few people love that person (L is really low), then, assuming the person is dissatisfied for no one loving them, H should be low as well.
That's algebra.
So? You're just naming a variable love, and another happiness. That doesn't make math love or love math in any way.
Quote from: Clavin12 on November 20, 2009, 07:26:29 PM
So? You're just naming a variable love, and another happiness. That doesn't make math love or love math in any way.
No he is quantifying. Get it right.
Quote from: Clavin12 on November 20, 2009, 07:26:29 PM
So? You're just naming a variable love, and another happiness. That doesn't make math love or love math in any way.
Read a post completely before replying.
I tried this equation on my PC, looked what happened
(http://halshop.files.wordpress.com/2007/03/phpw9jvl0pm.jpg)
Quote.99999...... is exactly 1. Let me prove it...
x = .999999999...
Multiply both sides by 10
10x = 9.999999999...
Because x = .99999999..., let's subtract it (x) from both sides
9x = 9
Divide both sides by 9
x = 1 = .999999...
this calculation was interesting to me, but it took me awhile to find out what's wrong with it.
when you get to the point where you say, "lets subtract x from both sides" the equation no longer is true, since x = 0.9999999999... and 9 times x is 8.99999999999999999999.......999991 and is NOT 9, therefore the equation is false since x is not equal to 1, but is 0.999999999....
btw, you cannot change what x is equal to, after you have given it a value.
Quote from: Rocket on November 22, 2009, 02:40:10 AM
this calculation was interesting to me, but it took me awhile to find out what's wrong with it.
when you get to the point where you say, "lets subtract x from both sides" the equation no longer is true, since x = 0.9999999999... and 9 times x is 8.99999999999999999999.......999991 and is NOT 9, therefore the equation is false since x is not equal to 1, but is 0.999999999....
btw, you cannot change what x is equal to, after you have given it a value.
1. 9x is NOT 8.999...91, because the 9's go on FOREVER after the decimal point. Yes, (.999)*9 = 8.991, but .999 is finite. You cannot count the number of repeats after a repeating decimal, so you can't add a random number at the end. There is no end. It is also not possible to tuck infinite 9's between the decimal and 1. If that were true then I could tuck infinite anything into anything, changing their values completely.
I love it how people try to stop infinite. There is no stopping it because it is not growing. It's already infinite, and it always has been. It is simply forever. Humans are always trying to see infinite. Grasp the fact that you can't even think about reaching it. Just call it "infinite."
2. I never changed the value of x.
.99999999999... is the same as 1. They're the same number, just written differently:
x = 0
and
x = 0*(6)
I still didn't change the value of x. They're the same, just written differently.
I'm right about this. I promise. That proof I used isn't mine. It was taught to me in a math class a while back. I'm not the only one who knows this.
Quote from: Feared_1 on November 22, 2009, 06:08:23 AM
.99999999999... is the same as 1. They're the same number, just written differently
I'm sorry but no they are not. Graphically it is called an asymptote, look it up. It approaches 1 but never reaches it.
and AGAIN, .6' + .3' DOES NOT EQUAL .9' , it equals ONE.
There is no rounding, it is exact. I will bug one of my professors about an inductive proof for this just to set it straight.
Take a look at a reciprocal graph. The values all approach zero but never reach it, instead shooting off into infinity.
I know what an asymptote is, and you can't get one from .999... because .999... doesn't form a curve, it forms a straight line at y=1.
An asymptote is where a function does not exist... EVER. AHadley already brought up (1/x), for example. Because you can't divide by 0, the graph's domain will come from negative infinite and grow as the graph gets closer to 0. The range
does shoot off into positive infinite and continues again from negative infinite, NEVER touching 0.
Quote from: Nielk1and AGAIN, .6' + .3' DOES NOT EQUAL .9' , it equals ONE.
You're saying exactly what I just proved but you don't believe.
.6' + .3' = .9'
.9999999... = 1
Therefore, using the transitive property,
.6' + .3' = 1Let me give you something else to chew on:
.33333333... = 1/3
If what you're saying is true, then the above is
not true. .3333333... approaches 1/3, but never reaches it.
That's false. In fraction form, .3333333... is 1/3 EXACTLY.
In fraction form, .9999999... is 1 EXACTLY.
Quote from: Feared_1 on November 22, 2009, 06:55:21 PM
You're saying exactly what I just proved but you don't believe.
.6' + .3' = .9'
.9999999... = 1
Therefore, using the transitive property, .6' + .3' = 1
Let me give you something else to chew on:
.33333333... = 1/3
If what you're saying is true, then the above is not true. .3333333... approaches 1/3, but never reaches it.
That's false. In fraction form, .3333333... is 1/3 EXACTLY.
In fraction form, .9999999... is 1 EXACTLY.
No. 1/3 plus 2/3 is 3/3 or 1
0.3' + 0.6' again IS NOT 0.9'
0.3' + 0.6' = 1
I am NOT agreeing with anything you are saying. I am NOT applying the transitive property. It is simply that 0.9' is NOT the same number as 1. I think I would know after Calculus I, II, II, Statistics, Linear Algebra, and Discreet Math. Specifically Discreet Math.
EDIT:
1/3 is EXACTLY .3'
2/3 is EXACTLY .6'
3/3 is EXACTLY 1
0.9' is a mathematical fallacy on the part of the human. It does not occur. It is caused by assuming that two infinite decimals sum to another infinite decimal always. This is not the case. This would be like assuming that half of an even number is always an odd number.
Tell me when y=(-(1/x))+1 and .9' intersect?
I can tell you.
Infinity.
NOT UNDEFINED.
They intersect at in infinite distance, but they do intersect.
But if (-(1/x))+1 intersects a line that has no slope of any kind, and it itself never reaches 1, then neither can that line it intersects.
If that line was equal to 1, then the point of intersection would be undefined.
This is why calculus works. Sooner or later, you split enough hairs to the point where it is moot.
I AM applying the transitive property because it is CORRECT. What part of my previous proof do you not understand?
.999... has INFINITE 9's at the end of it. INFINITE. You can't stop infinite! It is equal to 1.
http://en.wikipedia.org/wiki/.999
Quote from: Feared_1 on November 22, 2009, 07:40:03 PM
I AM applying the transitive property because it is CORRECT. What part of my previous proof do you not understand?
.999... has INFINITE 9's at the end of it. INFINITE. You can't stop infinite! It is equal to 1.
http://en.wikipedia.org/wiki/.999
No you cannot stop at infinity, you can only approach it... You should know this.
Well exxxxxxcuuuuuuse me for assuming we were using exact math and not using the "there are no nonzero infinitesimals" property. I find it interesting that Wikipedia (a bad source int he first place) still only notes when it comes to the pure mathematics that 0.999' ≈ 1, which I have no quarrel with.
In reality this all stems from the misunderstanding that 0.3' + 0.6' = 0.9', a common academic claim. As I have been saying all along, .3' + .6' = 1, not .9'. Thus there is no need to argue that .9' is = to 1. Claiming it is is simply the continuation of confusions and propaganda that has existed since calculators became commonplace.
Do note that you are summing two infinitely long decimals, think about that.
Maybe I should write this differently for you.
0.9' ≈ 1.0'
It is called an infinitesimal. You might want to ignore it, simple math may want to ignore it, but it is
THERE.
I will now take the time to disprove some proofs to the contrary.
0.999... = 9/10 + 9/100 + 9/1000 + ...
and the sum of the geometric series on the right is
(9/10)/(1-1/10) = 1.
This is actually true, but the meaning of geometric series is misused. The series tells you what it approaches, but not always exactly what is is. Linguistic and mathematical trickery.
Quote from: Not sure about this onex = 0.999...
multiply both sides by 10
10x = 9.999...
subtract the first equation from the second
9x = 9
so
x = 1
This exploits the base 10 system, so let us do base 2.
x = 0.111...
multiply both sides by 10 (that is binary 2)
10x = 1.111...
subtract the first equation from the second
1x = 1
so
x = 1
So this also says that binary 0.1111 is the same as binary 1? 0.111 is just barely above 1.5 in decimal. Sounds suspicous to me.
I would also like to note how calculators work. They actually do limits and such, and decide what number a value fast approaches. This is why some calculators spit out .999 and others 1. It all depends on what extra programming they have on top and how far they plan to approach infinity in their calculation.
I will get some more later.
Looking at how ridiculous and frivolous this argument gets (as per my investigation of it on other sites) I think another so called mathematical fallacy should be brought up.
You should know better than to bring a massive forum flame-pile of a problem here...
Hmm, you're approaching this from a different direction than I am. You are using limits and I am plugging in "∞."
Because of this, we'll never really reach a conclusion... but oh well.
Sorry if my tone is overly critical, I don't mean to be intense, I'm just having a blast :D
1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... = 1
Geometrically:
This isn't what we're talking about, but it's the same concept. Take a full square, split it in half. Split that half in half and you get a 4th, split the 4th in half and you get an 8th, split that in half and you get 1/16 and so on and so on FOREVER. If you do this for infinite (not a really big number), you end up with small bits and pieces of the full square. It is impossible to split it in half any longer after you have split it in half for infinite, even though it doesn't stop.
I'm not trying to analyze infinite by giving it a value. I have given up doing that. I am saying that infinite is forever and there is no valid attempt to analyze it any further.
Similarily, 1/2 * 2/3 * 3/4 * 4/5 * 5/6 * 6/7 * ... = 0
"..." doesn't mean go on for a super long time and find out what it approaches, it means do that for infinite without using limits. If you do do it forever, you WILL get 0 as an answer. It is impossible for humanity to do it, but that's what you'll get after forever.
EDIT: in response to your last post:
As far as I'm aware, we're not flaming. I choose not to jump into flame wars, and if it ever were to get there I would step out. I agree, there is no end to this argument (it goes for infinite :lol: ). It all depends on how you interpret the math and that's different for everyone.
The last 3 years of my math has been 'approaching' infinity and zero, you can understand why I have the view I do.
God I am sick of limits.
Quote from: Nielk1 on November 22, 2009, 09:55:51 PM
The last 3 years of my math has been 'approaching' infinity and zero, you can understand why I have the view I do.
God I am sick of limits.
I totally see your side of the argument. Your view is that "you can't get to infinite, so find the limit." That's valid math.
My view is "you can't get to infinite, but the 'limit x -> ∞' is the same answer as if you plugged in '∞' for x." Also valid math.
Basically, my view is "just give up" and yours is "don't even try." All depends on how you interpret things.
AHadely, you should be ashamed of the mess you created! :P
QuoteIf you do do it forever, you WILL get 0 as an answer.
Hmm no. The Universe is made of something and nothing. Non zero +numbers represent the something, zero represents the nothing. 0 is infinite in its non-existence, no amount of multiplying will alter that state at all, equally no breakdown of non a zero number will result in 0.
0 is not a number, it is the "paper" on which all other numbers or things are written.
Mathematics must represent the Universe that allows it to exist, otherwise it is just nonsense.
So next time you do a calculation that ends up with a - answer, ask yourself how that is possible.
the base (get it? heheh) problem i think is that you usually don't do proofs with repeating decimals anyways, because by definition they are so inaccurate. Usually you stick to the fraction because they're absolutely precise.
Quote from: mrtwosheds on November 22, 2009, 10:32:26 PM
So next time you do a calculation that ends up with a - answer, ask yourself how that is possible.
Instead of giving it for me to do, you should do it yourself! :)
I'll do it this time...
1/2 = 1/2
1/2 * 2/3 = 1/3
1/2 * 2/3 * 3/4 = 1/4
1/2 * 2/3 * 3/4 * 4/5 * 5/6 * 6/7 * 7/8 * 8/9 * 9/10 = 1/10
1/2 * 2/3 * ... * 29/30 = 1/30
1/2 * 2/3 * ... * 99/100 = 1/100
1/2 * 2/3 * ... * 999999/1000000 = 1/1000000
1/2 * 2/3 * ...forever = 0
Where x is the product.
If I were to use a limit:
lim(x -> ∞) = 0
The longer I go, the closer the answer gets to 0. If it goes on forever (which is not humanly possible), the answer you get
will be 0.
Quote from: mrtwosheds on November 22, 2009, 10:32:26 PMask yourself how that is possible.
It's not possible for humanity, but mathematically it is because math
can do infinite.
I understand that you're confused. Try to stop trying to give infinite a number value and just accept the fact that it is never-ending and it will become MUCH easier. :-)
Quote from: Feared_1 on November 22, 2009, 10:03:37 PM
Basically, my view is "just give up" and yours is "don't even try." All depends on how you interpret things.
No, "don't even try" is MY view.
I was talking to Nielk1 in that post.
I know, and I was correcting you. His view tries. Mine doesn't.
You're missing the point, obviously. Read it in the context it's placed in.
Quote from: eddywright on November 21, 2009, 04:06:56 AM
I tried this equation on my PC, looked what happened
<image removed in case it gives any of you bad ideas... :)>
OMG that was TOO funny... I love it...
-Av-
Quote from: Feared_1 on November 23, 2009, 02:46:23 AM
You're missing the point, obviously. Read it in the context it's placed in.
I did, when i read it the first time.
Then read it again, because you still don't understand what I meant by that.
I'm done here :| The topic is about math fallacies, not explaining what a mathematical view means.
Maths teacher finally admitted that this whole thing works because of the divide by zero :lol:
No I do understand what you meant, it's just that my meaning is different than your meaning.