How to equate 2=3?

I have 5 points to make:

1. This is the most ridiculous thread ever.

2. there are no bugs in math. the only bugs that exist are the ones people come up with

3. The visual basic function sqrt(25) will return 5. the actual mathematical operator would return ±5 (plus OR minus 5, not both)

4. If -2 = 2, i would be very rich, and i'm not.

5. Any number over 0 is absolutely absurd. if you have 20 apples, and give each of your friends 0 apples, how many friends could you have? None, becuase you're cheap.:D

Woah! Nobody thought I was actually serious do they? I was just making up bloomin' bollocks to keep this thread going.... Who really cares if this thread's heading nowhere, is it your business to say it sucks? Even if it is, what's stopping us from saying you suck... some people's opinions are best kept to themselves! Others should be blurted out at the wrong time! :D

Oh, and David, We all know what you meant though, I'm just a picky guy.

snakeeyes1000,
I've apologised for 3. already! Happy now?!
If 4. was correct, and 2=-2, then society would not exist like it does. Your bank account would be in debt. And missiles would go all over the place.

my math teacher would panic in this forum. he would say

2 == 2
3 == 3

there is no way around it without intentionally screwing your math

By David Hooper:

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If 4. was correct, and 2=-2, then society would not exist like it does. Your bank account would be in debt. And missiles would go all over the place.

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ACtually, your account would be in debt AND profit at the same time, and if you bought something the seller would ALSO owe you the same amount.

Oh, and you'd be older AND younger than everyone else, and you could claim that you were always below the speed limit, but you could also be said to be too young to drink or drive :D

To try to change the topic, you actually can have a right angle equilateral (I think I spelled that wrong) triangle. Just not on a flat surface. Take a sphere, cut it in half, cut that in half, and cut that in half (1/8 of a sphere). You have a right angle equilateral triangle. You can also draw one onto a balloon. 270 degrees in a triangle:D.

I know that someone is going to say that it has to be a flat surface, but that seems slightly ridiculous to me: if you have a triangle drawn on a piece of paper and the paper bends, does the triangle cease to be a triangle?




Back to the original topic, I think that the proof that 2 == 3 might be the hotel story thingy.

Three men rent a hotel room for $30, each paying $10. After they're in their room, the hotel owner gives the bellboy $5 to return to them because it was only supposed to be $25. So in order to prevent fighting, he keeps $2 and gives each of them $1 back. So, they each paid $9, for a total of $27, and the bellboy has $2, giving a grand total of $29. Where's the missing dollar?

I'm sure I remember seeing this used to show $2 equalling $3 (although of course it doesn't;))

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Originally posted by Alphanos
To try to change the topic, you actually can have a right angle equilateral (I think I spelled that wrong) triangle. Just not on a flat surface.

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Um, I'd have to say that this isn't a triangle anymore - unless you have a very open definition for triangle to include lines that aren't straight. However, I could be wrong.

Off to bed I go - too much Warcraft 3 :D

Destined.

The line is perfectly straight, its the surface that isn't:).

when you bend the paper, it ceases to be a 2-dimensional figure and enter's the third dimension, depth. So no, it, by definitition, is nothing more than a 3 curved lines, connected.

that debunks your logic.


M1|M2|M3|HO|BE
--------------
10|10|10|00|00
00|00|00|30|00
00|00|00|25|05
01|01|01|25|02

But where's the other dollar?





... just kidding!

I've got the dollar here... But if 2 = 3 then I have all the other dollars too.

each man has a dollar, the bellboy has 2, and the hotel has 25. This is no paradox, it's an inneficiency of the english language rearing it's uglier-than-usual head.

You know, people who don't know what they're talking about shouldn't bother replying to this thread...

The 2 = 2 thingy:
2 = 2
so 4 = 4
but if you square root that, you get:
EITHER
2 = 2
OR
-2 = -2
NOT a mix between the two (Such as 2 = -2)

The ONLY way you can equate 2 = 3 is by dividing an equation by zero, which as everyone might have realized is impossible to do (see http://www.vbforums.com/showthread.p...&pagenumber=3, near the bottom, posted by me). The principal there can be applied to equate 2 = 3 by simply adding 1 to both sides of the result.

If you can imagine the flaw in this thing:
If 2 = 3, then 1 = 1.5, simple enough I think. But if I actually had one dollar, then that would be 1.5 dollars. But that 1.5 dollars = 1.5 * 1 dollars, which is the same as 1.5 * 1.5 (if of course 2 = 3). You see the problem is if you kept going on like that you could have an infinite amount of money.

It's not a problem with the maths, it's just humans bending the rules. Maths says you CANT divide by zero, but if we DO do that, how can we blame maths when it all goes wrong?

Mr. Snake Eyes is almost right with the triangle on a curved surface thingy...

Except:

The triangle is STILL two-dimensional. You are however putting a two-dimensional triangle into a three-dimensional world. This necessarily distorts the angles and lengths of the figure (in this case I think the angles are all made smaller by a factor proportional to the curvature of the surface you're putting it on to relative to a flat plane, but DONT quote me on that).

Gordon Bennett

Just need some clarification

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The 2 = 2 thingy:
2 = 2
so 4 = 4
but if you square root that, you get:
EITHER
2 = 2
OR
-2 = -2
NOT a mix between the two (Such as 2 = -2)

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You are closer to what I said before.

LHS 4 is different from RHS 4

4 = 4

if you square root that you get

2 = 2

or

-2 = -2


Can I assume like this

2 = -2

or

-2 = 2

Bcos there is no rule that if LHS has a +ve root RHS also should have +ve. Please keep in mind that you are not multiplying -1 or +1 on both sides. You are taking roots on both sides. There is no mix between LHS & RHS.

+2 & -2 are two roots of 4. Either one can be subtituted for root as you said.

Just analyse a little bit more. I can correct myself if I am wrong in my comment.

You're absolutely right vsusi! Give me your number, I'm looking for a used car, and who better to buy a car from than someone who charges -$1000?

The square root of 4 is either 2 or -2. That means 2 x 2 or -2 x -2. That does not include switching them.

You're trying to find a flaw in mathematics, when the flaw is in the enlish language. Get over it.

vsusi:

You said: "Bcos there is no rule that if LHS has a +ve root RHS also should have +ve."

That's complete crap:

Root(2) = ±2

So from Root(2) = Root(2) u get:

±2 = ±2

That 'plus or minus' sign is not interchangeable, i.e. either they are both plus or both minus, not a mix.

If I wanted to say -2=+2 or +2=-2 then I would turn one of the signs upside down so that it was 'minus or plus' (in order from the top).

However the square root function of mathematics doesn't do that, it does what's written above.

Gordon Bennett

What is Crap?

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Root(2) = ±2

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LOL

Nishantp

Thanks for your post.

That is what I need.

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2 x 2 = -2 x -2

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2² = (-2)²

Take square root on both sides.

(2² )^1/2 = ((-2)²)^1/2

Now 2^2/2 = (-2)^2/2

2 = -2 (Proved)

Thanks again.

actually, vsusi, I'm not completely clear on this, but you have to simplify

((-2)^2)^(1/2)

into

(4)^1/2

You must start from the inside out. Then you get

4^1/2 = 4^1/2.

Which, of course, is exactly correct. If you don't follow the rules of math, like order of operations, you can get whatever you want.

ok, first of all, do not ever check a mathematical term in a english dictionary, lol. use a math dictionary (the Square root thing in ditionary.com is absolutely hilarious and of course wrong). sqrt(x) is defined to be the *NON-NEGATIVE square root of x*. it may seem logical to include the negative sqrt as the answer to sqrt(x), but it is most definately wrong!!!!

if you want to solve x^2=c, or x^2=y^2, do difference of squares
if c<0, there is no real solutions for x.
otherwise (x+sqrt(c))(x-sqrt(c))=0 => x=sqrt(x),-sqrt(x)
x^2=y^2
x^2-y^2=0
(x+y)(x-y)=0
x=y, -y

what you fail to realize that x is a VARIABLE and 2 and 3 are constant values. you can not treat a 2 as a variable.


some common math newbie mistakes (these are the mathematical definations, not some made up stuff, so don't bother argue them)

1. you can't divide by 0, period.
2. you can only add 0 or mulitiply by 1 to an equation.
3. constants are NOT variables. don't treat them like one!
4. function by definition returns exactly one value. otherwise it is not a function. domain restrictions are placed to ensure that this happen!!
5. sqrt root is a function. sqrt is defined to be "The NON-NEGATIVE square root of a number". its domain restriction of f(x)=sqrt(x) is that x>=0
6. infinity is not a number. don't treat them like one!
7. rules that applies to real numbers does not necessary mean that they also applies in imaginary and complex numbers

btw for your cutting up the sphere thing, there is this thing thats called spherical triangles, namely triangles that are drawn on spheres (so the side would be curves). rules of triangles does not apply to spherical triangles. i can draw a spherical triangle with 3 right triangles. i think that if you place two of the vertices would be the north and south pole and the third would be any point along the equator to form such a spherical triangle (i am not 100% sure). there are no 3 dimensional triagles. there are only tetrahedrons in 3D.

SnakeEyes

Mathematics says.

If there is a Power to a Power, you can multiply both powers.

(ie) (a^X)^Y = a^{X x Y}

This is also correct according to mathematics.

BTW you said you were not clear but where did you find the error?
:D

Yeah, 'crap' is an English synonym for '$h1t' or 'poo' which is ruder than poo so you feel better after saying it, but not as rude as $h1t so you can use it in public restaurants.

you treated the constant as a variable. you should do the squaring first. so snakeeyes is right

when it comes to x^(2/2), the answer will still be x.

fractional exponents law says you take the sqrt first, then square it.

so it would be (sqrt(x))^2
since x could be less than 0, sqrt(x) could be imaginary. but squaring the value would get your original x back.

Values (Numbers) should be substituted for variables.

Variable is defined in Mathematics as Having no fixed Quantitative value.

IMHO Equations with Variables are templates for substituting with any value (numbers).

(eg) Take any calculator and you will see X^Y. That means X has to be substituted by first number and Y by the next number.

Same way creating functions (with parameters) in a computer program. Parameters are substituted by values.

If you are right then all the Theorems and Equations in the world will be non-sense.

Don't get confused with Constants and Variables.

lets look at derivitives:

f(x)=a^x
g(x)=x^a

so according to you, there is no difference between variables and constants so f'(x)=g'(x)
but in reality is not.

looking at another function:

f(x)=0/x

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Equations with Variables are templates for substituting with any value (numbers).

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according to you i can substitute x=0 into the function. but in reality i can't because you can't divide by 0. Why can't I? because the function itself have domain restrictions.

same with the square root function.

my point is that if you got a bunch of constants, evaluate it to avoid trouble cause if you treat it as a variable, you might cross a boundary and does something you can't do. usually you won't have trouble replacing a variable with a constant. but at some special cases you will.

for this specific problem,

if you just look at the algebra:
(x^2)^(1/2)
since x^2 is non-negative, and taking it the principal square root of that number would also yield in a non-negative number - so the correct answer is abs(x)

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f(x)=0/x

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is valid even if you substitute 0. Only thing is you will get an error (In Calculator). Or Indeterminate or Infinity or -Infinity if you do manually. Thats it. It doesn't mean the function itself is wrong.

Acceleration = Velocity / Time

If you want to substitute 0 to Time, it is absurd. Atmost you will get an error (in calculator) even if you do that for fun. It doesn't mean that the formula itself is wrong.

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according to you i can substitute x=0 into the function. but in reality i can't because you can't divide by 0. Why can't I?

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You can substitute any number you want to a variable. That is why it is called as variable. If you cannot substitute then variable will also become constant. Then there is no meaning in calling it as variable. In my case I am not using 0. So we should stop this kind of argument.

Please don't try to insist your own theory here.

In Science(reality) they use infinity and 0 for doing lot of calculation. Infinity in science means a very big value and 0 means very small value. (eg) Even 2 miles can be infinity for ordinary Camera lens if it is not able to focus.

lol 0/0 (indeterminate) is not infinity nor -infinity. get your facts straight. you are talking about undefined.

it is a mathematical fact that you can't divide by 0. infinity is not a value. you restrict the domain so actions like that doesn't happen. why do you think calculator gives you an error? why not give you infinity? because infinity isn't a value to play around with. it is not possible to divide by 0. you can divide by
1X10^(-1X10^(1X10^999999999))) that would result in a really big number. but infinity is not a value!!

u can substitute these numbers. I can't stop you. math can't stop you. your boss can't stop you. but the answer you get has no meaning and you cannot work with them.

you can work with 1X10^(1X10^(1X10^999999999))) on the other hand, but what can you do with infinity? oh right, as C++ says it, NaN, or Not a Number.

right i should agree that we all live in a infinity time where an infinity things are possible. lol this is america you can have your own theories and beliefs. we are on the internet so there are even less rules to be bounded by so don't lecture me about it.

Cool Bugz

Infinity is based on context and not based on just value.

Infinity cannot have a constant value.

In the following link you said

http://vbforums.com/showthread.php?s=&threadid=188573

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having a size or absolute value that is greater than any natural number (or growing out of all bounds).

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It need not be greater than any natural number.

Take 1 drop of poison and mix in a pool of 10,000 Cubic meters. Even though 10,000 is finite nobody is going to die if he drinks it because for 1 drop of of poison 10,000 is infinite(very huge value).

For a camera lens or eye lens even 2 or 5 miles can be infinite even though they are finite.

Dish or DirectTV and all satellite stations works with the same principle too. Distance between your dish and satellite is finite and not infinite. But for your dish that distance is infinite.

BTW I already know that 0/0 is indeterminate (I have already posted in one of the math threads long back). I was just giving you an example. :D

If you do not consider Infinity even after this please consider atleast now IMHO.

I think we are going out of topic. This is just a discussion about a real mathematics and unreal fact (like 2 = 3).

Thanks for your participation.

Infinity is not a number, it's a concept.

1/0 does not = infinity or anything else, it is undefined.

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for 1 drop of of poison 10,000 is infinite

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That's incorrect: 10,000m³ is not infinite, it's just a lot bigger than 1 drop. 10000¹⁰⁰⁰⁰m³ isn't infinite either, relative to the drop or otherwise. If infinity could be measured (which it can't because it's not a value), it wouldn't be measured by how much a drop of poison needs to dilute in water to not kill someone, where do you come up with that crap?

Vsusi most of what you say is bollocks: stop arguing, for your sake and ours.

I admit. That example may be wrong or I don't know how to explain. But not all.

You guys may be Math & Science genius. Definitely not me.

But 1/0 is not undefined. It is +Infinity for my knowledge(Even though limit for infinity is undefined). But the answer is +ve and huge.
http://mathworld.wolfram.com/d2img1616.gif

Even based on limit concept

http://mathworld.wolfram.com/iimg972.gif

Similarly

http://mathworld.wolfram.com/iimg971.gif

There are some more concepts related to infinity like
Countably Infinite, Continuum, Finite, Infinite, Transfinite Number, Uncountably Infinitem, etc.,

The following is just for fun
Pour 1 x 10^-Infinity ml of poison in that pool instead of 1 drop.:p :p :p

1/0 is undefined, and it definitely is NOT infinity. Infinity cannot be evaluated. If 1/0 = infinity then what's 2/0? Bigger 2x infinity?

OK consider this:

if 1/0 = infinity, then that's equivalent to saying 1 = infinity x 0.

Think about that one then!

Mathematica refers to divisions by zero as 'Complex Infinity'.... I dunno. But, Masterbandit666, even if 1/0 = infinity, 2/x will share a similar limit as 1/x, it will still approach infinity as x->0. Same goes for all positive real numbers as a numerator (I would think).

I just try to avoid devisions by zero for all the reasons stated here.

Good Catch by Masterbandit666.

For me Infinity x 0 will lead to indeterminate. (Since Infinity = 1/0)

1/0 x 0 = 0/0 x 1 = Indeterminate (which should mean any +ve number. Can be 1, 2 or n) because any +ve number divided by 0 is infinity.

So 1/0 = infinity, 2/0 = infinity and n/0 = infinity.

I guess Parents yeild Children and not vice versa.

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1/0 x 0 = 0/0 x 1 = Indeterminate

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you cannot treat 1/0 as a number because it is, and take it at face value: UNDEFINED!

I've been at work a lot lately... not much time spent here. excuse me. Let's consider what division is. Division is actually just multiplying by the inverse, correct. Look at the following statement.

x/y

can ALWAYS be rewritten(for all real numbers) as

x*(1/y)

The only exception to this rule is that y must have a real number multiplicative inverse. Therefore, as it is plain to see, mathematics disallows the value of y from ever being 0. You can see why as the value of y decreases, the quotient increases. Therefore, as y approaches 0, the product grows without bound. But it can never actually be 0. That would be undefined. If in a problem, you correctly reach a solution divided by 0, you automatically know that the question has no answer. If anyone wishes to argue with this, argue with my logic, not the math. The math is correct; I might not be.

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Originally posted by snakeeyes1000
Therefore, as it is plain to see, mathematics disallows the value of y from ever being 0.

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Is it maths or is it humans? lol, just kidding. :D

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2. there are no bugs in math. the only bugs that exist are the ones people come up with

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Am I the only one who reacted to this?
Mathematics seems to be flawless, and for more than two millenniums (as long as everyone keep out of the "When does the millennium start-question) people thought it was beyond doubt that pure logic reigns over the math.
This thought means that once a mathematical theory is proved, using only the ten postulates from Euclides and logical rules derived from them, nothing could threaten this theory. Similarly, two theories that both have been proved according to the rules cannot contradict each other - if they do, [at least] one of them must have an error we have overlooked.
This thought, or rather way of thinking, also opens up for an "end" of mathematics - with enough thinking power, possibly with the help of logical and advanced computers, all mathematical theorems can be proved.

However, the Czech-born mathematician Kurt Gödel in 1931 proved, that we cannot prove the mathematics to be flawless!
He didn't say there are flaws in mathematics, but he did say we cannot rule them out - only pray we never find any.
This is because every set of rules and derived proofs have to rely on each other, and can therefore not be proved independently.

This means that we cannot be sure we will never find a set of rules for right angled triangles which contradicts Pythagoras but nevertheless is true. And if that happens, some math teachers are going to have some serious rethinking of marks to do...

So what's the point? We have still not found any bugs in mathematics, there seems to us there are none, but we cannot prove it. There might be bugs in mathematics!

To add to the misery of all this, Gödel later developed paranoia and starved to death when his wife underwent treatment for some disease in hospital. He was afraid of getting poisoned, and refused to eat anything she hadn't cooked.

That's what happens if you meddle with Mathematics.
Pentax

I must say I can't argue with that!

I have an idea, lets let the people who think 2 = 3 live their lives spending $2 and buying something worth $3, and develop an overdraft. According to their logic, the bank will begin to owe them money and they will get more money. Of course, the more sensible ones already know that 2 != 3, so whenever we go into overdraft, we know that we owe the bank money, rather than vice versa.

Which group of people will be better off? The people who can count? Or the people who can't?