I might have just disproved math.

[asacatman]

My half-assed way of making my Calc teacher hate me, is to take the limits of indeterminates and claim that's the answer. For instance:

(inf = infinity)
0 / 0 =~ 0.00000000001 / 0.0000000001 =~ 1 (Therefore 0 / 0 = 1)
0 ^ 0 =~ 0.00000000001 ^ 0.0000000001 =~ 1 (Therefore 0 ^ 0 = 1)
0 ^ inf =~ 0.00000000001 ^ 999999999999 =~ 0 (Therefore 0 ^ inf = 0)
inf ^ 0 =~ 9999999999999 ^ 0.0000000001 =~ 1 (Therefore inf ^ 0 = 1)
0 * inf =~ 0.00000000001 * 999999999999 =~ 1 (Therefore 0 * inf = 1)

I'm pretty sure there are answers to these (though I'm probably wrong), since L^Hopital Rule is pretty much an indirect way of solving indeterminates. But whatever, I'm too lazy to do anything with that. It's the weekend.

I don't get it. How is saying that something very close to 0 divided by anothing thing very close to zero=1 mean 0/0=1? Am I missing something? I haven't done limits or analysis in shcool yet, so...

EDIT: Doesn't matter. Cerdog, who quoted you, has convinced me you are probably wrong, sorry.

 

[BehattedWanderer]

Ahhhh, that's adorable! You think you did something amazing. Did you make a little medal for yourself out of a bottle cap and a safety pin? Because you totally should.

Dividing by zero isn't an actual operation. You might as well be trying to divide by carrot. But, since you came all this way, you want to see a neat trick?

0[sup]0[/sup]=1

Neat, right? Nothing, to the power of nothing, is something! Something can be created from nothing! Math proves it!

[Just because you can apply the rules, doesn't mean the rules apply.]

 

[Blade1130]

... I'm really not good at riddles apparently. I can't figure your's (or even my own out). I will assume your calculations were correct for my riddle but we still have a issue. Logically, the way the problem is stated one one theorize that the hare and tortoise never meet up but physics as well as common sense tells us otherwise.

One can use the concept of the Harmonic Series to prove this but I can't for the life of me find it in my damn Calculus notes.

I'm sorry, I can't find a way to solve your riddle.

Note: Pardon the delay, had to feed myself.

Your riddle was really just a physical example of the halfway paradox (there is a better name but for the life of me I cannot remember it). If I walk from point A to point B, I must at some point reach a half way point, but before I reach the half way point, I must reach the 1/4 point, but before I reach the 1/4 point, I must reach the 1/8 point and so on. By this logic I cannot move because I must always reach a half way point of my intended destination.

That's not quite correct. Infinity isn't a number, so it's quite hard to use it in a situation like this, but the size of an infinity depends on the cardinality. For example, the natural numbers (0, 1, 2, ...), the integers (... -2, -1, 0, 1, 2, ...) and the rational numbers (fractions) are all the same "level" of infinity; as weird as it sounds, they are all the same size. On the other hand, the real numbers are larger.

True, infinity is not a number, it is a concept, and this makes it difficult to use mathematically. However this is not impossible. 1 + x > x for all real values of x. You might say infinity is not a real value, therefore the previous equation does not apply, which is somewhat correct. But lets think about that statement, Pi is not a real number. sqrt(2) is not a real number. sqrt(-1) is not a real number. But isn't Pi + 1 > Pi? Isn't sqrt(2) + 1 > sqrt(2)? Isn't sqrt(-1) + 1 > 1?

Consider the example of 0 / 0. It is not a real number and the equation (0 / 0) + 1 > 0 / 0 is debatable at best. However we can think about this in terms of limits and approximate an answer. As I've said previously 0.00000000001 / 0.00000000001 = 1.

Graph y = x / x and check the value at zero, you will get a hole in your graph. But as an old teacher once said to me, this does not mean that the answer does not exist (DNE). It instead means you're going about it the wrong way. y = x / x can be simplified to y = 1, therefore y(0) = 1 as I said above.

If you do the Lim[sub]x->0[/sub](x / x) you will get DNE as an answer. Unsolvable right? Wrong. As I said a couple posts back this is a very easy L'Hopital Rule problem, derive the top and bottom and you get Lim[sub]x->0[/sub](1 / 1) = 1.

Didn't I just prove that 0 / 0 = 1 three different ways? As such, the question of (0 / 0) + 1 > 0 / 0 can be proven by substitution. 1 + 1 > 1, I hope no one doubts that part.

I can't help but feel I'm going off-topic, you said that infinity + 1 = infinity because the infinity overpowers the 1 and can be simplified to infinity = infinity. However, let's look at it on a smaller scale. 0.0000000001 + 1 != 1. The 1 greatly overpowers the decimal, but it still has an effect. 1 + 0.000000001 > 1 no matter how small you make that decimal. In fact, lets make it the SMALLEST decimal, 1 + (1 / inf) > 1. Common sense will tell you that 1 / inf is the smallest positive number, since, isn't 1 divided by ANYTHING a positive number? It's a dammed small number, but a number nonetheless. If I could type this, I would say (1 / inf) equals 0.0(repeating)1. However, no matter how many decimal places you go, if you add 1 to an infinitely small number, you will still get a number greater than one. You can use this same logic to the infinity + 1 = infinity problem. No matter how big infinity is, if you add one to it, it gets bigger.

Infinity + 1 may equal infinity, since infinity + 1 can be simplified to just infinity. But that depends which level of infinity you use, as you said yourself. Infinity is not just a really big number, it also 1 + that number, it is also 2 + that number, it is also 1 million + that number, it is that number to the power of that number. Infinity holds an infinite range of values, none of them equal to one another, but all of them equally reachable.

A final example would be:
(2 * inf) - inf = inf (Because infinity is not being redefined mid-equation)
but
inf + 1 != inf (Because infinity is changing on the left side, but not the right, an algebraic impossibility.)

0[sup]0[/sup]=1

Calculus says that 0[sup]0[/sup] is indeterminate. Officially, 0[sup]x[/sup] is 0 for all x, right? By that logic 0[sup]0[/sup] = 0. But x[sup]0[/sup] = 1 for all x, right? By that logic 0[sup]0[/sup] = 1. There are two rules of mathematics here that are fighting each other. Therefore the answer is considered indeterminate. Although if you take my limit answer, 0.0000000000001[sup]0.00000000000001[/sup] = 1. I have yet to have a mathematician validate this, but I have yet to be proven wrong as well.

[Just because you can apply the rules, doesn't mean the rules apply.]

As much as I disapprove of the context of this statement, I like it. I'm going to have to remember that one.

 

[Cerdog]

True, infinity is not a number, it is a concept, and this makes it difficult to use mathematically. However this is not impossible. 1 + x > x for all real values of x. You might say infinity is not a real value, therefore the previous equation does not apply, which is somewhat correct. But lets think about that statement, Pi is not a real number. sqrt(2) is not a real number. sqrt(-1) is not a real number. But isn't Pi + 1 > Pi? Isn't sqrt(2) + 1 > sqrt(2)? Isn't sqrt(-1) + 1 > 1?

Pi and sqrt(2) are both real numbers. sqrt(-1) is not, and the last inequality doesn't make sense, because there isn't a notion of "greater than" for complex numbers.

Consider the example of 0 / 0. It is not a real number and the equation (0 / 0) + 1 > 0 / 0 is debatable at best. However we can think about this in terms of limits and approximate an answer. As I've said previously 0.00000000001 / 0.00000000001 = 1.

When you're dealing with things as awkward as 0/0, approximating isn't really that useful unless it's by limits, which we get onto in a moment.

Graph y = x / x and check the value at zero, you will get a hole in your graph. But as an old teacher once said to me, this does not mean that the answer does not exist (DNE). It instead means you're going about it the wrong way. y = x / x can be simplified to y = 1, therefore y(0) = 1 as I said above.

It can be simplified to y = 1 provided x =/= 0, partially for this very reason. You can't really make blanket statements like that.

If you do the Limx->0(x / x) you will get DNE as an answer. Unsolvable right? Wrong. As I said a couple posts back this is a very easy L'Hopital Rule problem, derive the top and bottom and you get Limx->0(1 / 1) = 1.

Didn't I just prove that 0 / 0 = 1 three different ways? As such, the question of (0 / 0) + 1 > 0 / 0 can be proven by substitution. 1 + 1 > 1, I hope no one doubts that part.

No. I've already discussed the first two methods, but the third is dubious as well. The entire point of limits is to avoid dividing by zero, particularly in calculus. For example, lim(x->0) (sin x)/x = 1, but that doesn't mean that (sin x)/x = 1 when x = 0. If it did, it would almost defeat the point of using limits in the first place.

I can't help but feel I'm going off-topic, you said that infinity + 1 = infinity because the infinity overpowers the 1 and can be simplified to infinity = infinity. However, let's look at it on a smaller scale. 0.0000000001 + 1 != 1. The 1 greatly overpowers the decimal, but it still has an effect. 1 + 0.000000001 > 1 no matter how small you make that decimal.

That's because 0.0000000001 is a number, and infinity is not.

In fact, lets make it the SMALLEST decimal, 1 + (1 / inf) > 1. Common sense will tell you that 1 / inf is the smallest positive number, since, isn't 1 divided by ANYTHING a positive number?

This has the same issue as the y = x/x thing from earlier. 1/anything is not always a positive number: for example, dividing it by -1 makes it a negative number. Dividing it by i makes it a complex number. You can't divide it by infinity at all, because you can't do arithmetic with infinity, because it isn't a number.

Also, common sense will often let you down in areas of maths like this, so it's not a justification.

It's a dammed small number, but a number nonetheless. If I could type this, I would say (1 / inf) equals 0.0(repeating)1. However, no matter how many decimal places you go, if you add 1 to an infinitely small number, you will still get a number greater than one. You can use this same logic to the infinity + 1 = infinity problem. No matter how big infinity is, if you add one to it, it gets bigger.

Infinity + 1 may equal infinity, since infinity + 1 can be simplified to just infinity. But that depends which level of infinity you use, as you said yourself. Infinity is not just a really big number, it also 1 + that number, it is also 2 + that number, it is also 1 million + that number, it is that number to the power of that number. Infinity holds an infinite range of values, none of them equal to one another, but all of them equally reachable.

I'm not entirely sure what point you're making here.

A final example would be:
(2 * inf) - inf = inf (Because infinity is not being redefined mid-equation)
but
inf + 1 != inf (Because infinity is changing on the left side, but not the right, an algebraic impossibility.)

Again, I'm not quite sure what you're trying to say. You can't do arithmetic with infinity at all.

 

[BehattedWanderer]

[Just because you can apply the rules, doesn't mean the rules apply.]

As much as I disapprove of the context of this statement, I like it. I'm going to have to remember that one.

Almost every doctrine has an example of "This rule always works!", with a giant asterisk that says "EXCEPT FOR [Y]CASE". It's from twisting the rules to make it apply that we have such fun but ultimately abstract concepts as "diving by zero" and "infinity". It's where we get our paradoxes. My favorite is the Banach-Tarski paradox, which demolishes the conservation of mass, but manipulating the volumetric data. It's subtle relationships that cause such things, but mathematically, they're sound. Realistically, they're useless. It's like looking at an Escher painting--your mind conceives that the shape is possible, but the shape remains impossible in three dimensional space. Just because it looks like it should work, doesn't mean it actually does.

 

[mcnally86]

I believe it's fair that I started calling bullshit when we started on imaginary numbers, as though working with ones that actually exist wasn't good enough.

Imaginary numbers are just a name, they aren't actually any more imaginary than the real numbers.
Physicists use imaginary numbers to solve real problems every single day. Without imaginary numbers we wouldn't have the monitors you're using to read the posts people make on this site, they have very real and practical uses.

The same is true of a lot of maths. It may start as someone's "cool idea", but so many many advances in science have come from maths that someone just made up for the hell of it. If mathematicians waited until maths was useful before they came up with it, then our technology would be at least 50 years behind where it is today.

That part was actually a joke, the imaginery VS real bit. However, I'm going to need some citation on the part of you stating that imaginery numbers have an application beyond thought experiment. Since 'i' is literally representing a paradox, and that this is actually the tamest aspect of math acting less like science and more like philosophy, it smacks of carelessness. "We didn't feel like figuring out where this leftover piece of the puzzle actually comes from, so here, have a Lowercase-I." This is where math sort of falls short for me. I understand the logic you place behind it, pass the course, and move on...but it doesn't cry out as the pinnacle of precision anymore. And Discreet Mathimatics is very much this. It's the metaphysics of math that gives way to some interesting thoughts, but it's not logic and it's not science anymore. You follow my meaning, right?

Ham radio operators live off imaginary numbers. A lot of electronic work requiring frequency use triangulation with j. BTW its j now not i. j got the job as the imaginary letter because the i could be confused with other letters used in electronic math. Basically you graph real numbers on the x line of a graph and the imaginary fellows on the y line. I won't explain why because I don't know your background in radio operation but the easiest example is the impedance of a wire carrying a signal can be calculated with the help of algebra and imaginary numbers.

Mathematicians use i, engineers use j. J is used in engineering because i already denotes electrical current. As a lot of AC power theory uses complex numbers, you can see how this would otherwise lead to confusion. But i is the normal letter used for the square root of -1.

You dirty mitigation, j is the only true letter. Capital I is current. But yes current is the reason I is taken.

 

[Sexy Devil]

I clicked on this thread because I was intrigued by the title. I then read 3 pages of people stating and restating that you can't divide or multiply (i cringed when I read "times" in the first post) and 3 pages of essentially calling the OP an idiot for thinking he has accomplished something remarkable in mathematics.

And no, you don't get credit for thinking about something incorrectly. I do however give you credit for posting something that openly leads you to criticism from strangers on the internet using anonymity as their badge of courage. However, anything divided by 0 will always be impossible to calculate. In philosophy (which I believe someone mentioned earlier) yes you would get credit for challenging what we know and pushing ourselves to think about understood concepts in different ways, but in math, not so much.

If someone showed this to me in real life I'd still call them an idiot. Not using anonymity as my "badge of courage" here, he's just using really flawed logic that a fifth grader would know.

 

[Blade1130]

Why is everyone so upset at the use of "times"? Is it that unusual of a word?

I mean, yeah it's probably better to say "1 multiplied by 3", but does seriously no one say "1 times 3"? Is it that uncommon? I say that all the time, no one's ever made a fuss about it before...

 

[SL33TBL1ND]

You can't divide by zero.

Yes you can, just not in the way that OP thinks he can [http://en.wikipedia.org/wiki/Asymptote].

 

[Womplord]

OP, you didn't disprove maths. What your working out shows is that x can be any number, which is true. It is a well known fact that 0/0 is an undefined number, just like any number divided by 0. I only skimmed over it, but your working out seems fine.

 

[Costia]

there is no number that is equal to 0/0
you should study about limits
it is possible to arrange that a limit that is going to 0/0 will be equal to any number you want
x/x, x->0 =1
3x/x, x->0 =3
etc..
the limit can also be arranged to be infinity or 0

0^x = always 0
x^0 = always 1
0^0 = undefined
sometimes it is defined as 0 or 1 for comfort of calculations

in the word problem its 27 -2 not 27+2 , ad 25$ is what the manager got for the rooms

 

[Omnific One]

You can't divide by 0...

 

[Zack1501]

Oh god, What have I done...

 

[3 legged goat]

no in the case of 0/x=0, 0<x<0 or x is greater than 0 and less than 0 but not equal to it.

 

[Zack1501]

Punch 0/0 into your calculator for me and see what happens. Nothing divides by 0, not even 0. Full stop. The end.

Ok, I get it I'm wrong(If you people actual paid closer attention to my post you would realize i didn't think it was true ether) But this answer pissed me off the most. You punch something into your calculator and it said error so you ignore it? You don't care why? Just because a calculator cant understand it does not mean thats the end.

 

[Olas]

First you divided by zero.
Then you multiplied both sides of an equation by zero.
Then you divided both sides of an equation by zero.

What did math ever do to you?

 

[3 legged goat]

Punch 0/0 into your calculator for me and see what happens. Nothing divides by 0, not even 0. Full stop. The end.

Ok, I get it I'm wrong(If you people actual paid closer attention to my post you would realize i didn't think it was true ether) But this answer pissed me off the most. You punch something into your calculator and it said error so you ignore it? You don't care why? Just because a calculator cant understand it does not mean thats the end.

It is undefined, therefore the calculator can define it.

 

[DiMono]

You lost as soon as you said 0/0 = x

Anything divided by 0 is indeterminate; it has no solution, thus there are no valid values for x. So your initial statement is false. However, we can move beyond that to 0=0x, which is perfectly valid.

But then you lost again when you said 0/x=0 even if x is 0. Again, anything divided by 0 is indeterminate and has no solution. Thus if you have x on its own as the bottom half of a fraction, x cannot be 0 (or infinity). It can be any other number, but neither of those two.

So as soon as you assert either of those statements to be true, your proof falls apart.