Any math geeks out there?

[onlyadream]

Okay, this was on a T-shirt:

1. x=y
2. x^2=xy
3. x^2-y^2=xy-y^2
4. (x+y)(x-y)=y(x-y)

5. ((x+y)(x-y))/(x-y) = (y(x-y))/(x-y)

therefore: (x+y)= y
so, if x=1 and y=1 then (1+1)=1

Now, if you go thru it you see that it's correct, but how can 1_1=1?? The only thing I can come up with is that x cannot equal y since (x-y) is in the denominator (in line 5) and that would be undefined. Am I right?

[Nye Bevan]

1. You are correct

Division by zero is undefined. You can only divide both sides of an equation by a non-zero number, so the flaw is in going from step 4 to step 5.

[Ptah]

2. division by zero is frowned on.

[Dr. Strange]

52. Very true.

[Jamastiene]

3. Division by zero is undefined, but 1+1 does = 1

...in digital electronics

1-4 are correct but 5 is not. division by 0 is undefined.

I still do not see how the shirt got the "therefore" (x+y)= y part...unless...

In binary math, 1+1 = 1 because + is used to represent OR, as in an OR gate. In an OR gate if either x or y is 1, then z is 1. It could be a play on numbers to represent an OR gate.

OR Gate

x + y = z
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 1

So, for this statement, as long as y on the left side of the equation is always 1, y on the right side of the equation will always be 1 ...no matter what x is. It only gives the one example of x=1 and y=1.

"therefore: (x+y)= y
so, if x=1 and y=1 then (1+1)=1"

in an OR gate this is true assuming y is always = 1

I believe the t shirt is playing with your mind with #5 and represents an OR gate at the end there.

[onlyadream]

4. This was just plain old algebra

not binary.
But thanks for bringing back memories (I used to be an EE).

[Road Scholar]

18. I think it's downright illegal. LOL

:rofl: :rofl: :rofl: :rofl: :rofl:

[Parche]

5. its a pev t-shirt

it means he is 6inches...

:rofl: :hi:

[El Fuego]

6. Division by zero = Infinity

Let's say you have 1/x, and x is approaching 0.

1/0.00000000000000000001 = 100,000,000,000,000,000,000.

As x gets closer and closer to 0, 1/x gets closer to infinity.

But, if x = y the equation is just 0=0 anyway, since you're multiplying the numerator on both sides by 0.

[Nye Bevan]

7. NO! That is a pet peeve of mine

Division by zero is NOT "infinity". Division by zero is undefined.

It *is* true that when x approaches 0, 1/x *approaches* infinity. But 1/0 does not "equal" anything at all, not even infinity.

(One of my geekier DU posts....)

[Ptah]

8. Division is simplified subtraction.

It is just counting how many twos are in eight.
8 divided by 2 is four.

8 - 2 = 6 :1
6 - 2 = 4 :2
4 - 2 = 2 :3
2 - 2 = 0 :4


I you want to divide 1 by 0, you will subtract an infinite number of times.

One divided by zero is infinity.

[HiFructosePronSyrup]

9. What's zero times infinity?

[Ptah]

10. I think zero times infinity is zero.

[HiFructosePronSyrup]

11. So if zero times infinity is zero, zero times infinity cannot equal 1.

Therefore, 1 divided by zero is not infinity.

You are incorrect. Any number divided by zero is undefined.

[Ptah]

12. Well, you've got me there.

I'm glad I don't do math for money.

:thumbsup:

[El Fuego]

13. In computer arithmetic, it's undefined. In physics and calculus, it's INFINITY.

In other words, if you're using a calculator you bought at Walmart, 1/0 will be undefined. If you're trying to quantify the physical world in terms of mathematics, 1/0 is INFINITY.

[Ptah]

14. I make things out of metal. Physics?

We don't do zero.

It hurts our brains.

In the shop the other day.

[Rabrrrrrr]

17. No, you are wrong - anything divded by zero is undefined.

It's not a matter of where one buys one's calculators.

In physics and calculus, dividing by zero is IMPOSSIBLE and therefore UNDEFINED. The only thing that physics and calculus allows for is dividing by x as x approaches zero.

But, as anyone who knows what the fuck they're talking about knows, as x approaches zero, x actually never becomes zero.

[El Fuego]

54. A black hole exists because of division by zero. Are they impossible?

The infinite vacuum of space is division by zero. Is outer space not a vacuum? The big bang theory of the creation of the universe is division by zero.

Let's just throw out modern physics altogether! There's no such thing as this you know: :nuke: :nuke: :nuke:

[Rabrrrrrr]

63. A black hole exists because of division by zero? In what universe?

Black holes exist because of gravity, not because someone "successfully" divided by zero or because matter somehow managed to divide by zero. That's beyond laughable - it's fucking ludicrous. And insane. And shows that you need to take a physics class.

And as utterly and bizarrely wrong as you are about black holes being created by dividing by zero, I won't even touch how much more ludicrously in error you are about the Big Bang having similar roots.

Let's just pretend our own version of physics altogether!

[PVnRT]

66. Wha?

Black holes exist because, for any star with a mass more than three times that of our sun, internal pressure will be overwhelmed by gravity, causing an implosion. It has nothing to do with dividing by zero.

The Big Bang was possibly nothing more than a small but nonzero-probablity quantum fluctuation in an already-existing universe.

[Random_Australian]

23. .... well, except "infinity" in physics is an approximation.

And damnit, I could prove it if I could show that hermitian operators, when used on wavefunctions that are of finite norm (ie. composed of only functions of finite norm in the hilbert space representation of the wavefunction) produce, when leftmultiplied by the conjugate of themselves and integrated over all space, a number that finite!

Hmmmm, actually, I think it can only become arbitrarily large as we take limits, which would in turn imply that physical observables are not infinite, which in turn implies that in physics, infinite = an approximation, always.


Hmmmmm. But then again, is QM complete? That is the question. (And the answer looks a lot like yes.)


Furthermore, in calculus, it should be just limits again. That's why you l'Hópital everything in sight when it does something zero-on-zero-y, because it's just limits.


(Just don't think about what happens to sine of one on x as x approaches zero)

[PVnRT]

50. No - the limit of 1/x as x approaches 0 is infinity

1/0 is undefined, regardless of your field.

[pokerfan]

19. but if anything divided by infinity is zero

then.... :shrug: Dr. Math has several http://mathforum.org/dr.math/faq/faq.divideby0.html">explanations.

[peruban]

44. Mathematics can't divide by infinity.

That's why we use calculus to approximate the behavior of a function as it approaches infinity, which isn't really a number anyway.

But, in fractions the larger the denominator the smaller the fraction gets. To put it visually:

1/10 > 1/100

[peruban]

28. Both zero and infinity are abstract philosophical numbers .

But to answer your question, any number multiplied by zero is zero. The reason for this is that you can't produce numbers when you don't count them.

In plain English, zero can not be divided into components. There is nothing to count since zero is not a quantity. You can split nothing into something.

Do you like the way I explained the issue without using the meaningless word "undefined"?

[peruban]

43. I think you just answered your own question.,

If you count infinity zero times you get nothing, since nothing has been counted the resulting number is zero. It works this way with all numbers, you can't pick apart nothing, it has to be something in order to be divided.

[Rabrrrrrr]

16. No, anything divded by zero is undefined. It is NOT infinity.

As the other poster said, dividing by zero is impossible - it's undefined.

It's only in limits that zero sort of works - that is, lim(1/x) as x approaches zero is inifnity; but if x reaches zero, then it's undefined. Impossible. Without reality. Can't be done.

[peruban]

30. Wrong.

"If you want to divide 1 by 0, you will subtract an infinite number of times."

This confuses calculus, which studies rates of change, with algebra which is a set of operations defined over "field.".

[struggle4progress]

20. You're wrong, of course. Here's the proof:

Note: the proof will easier to understand, and more convincing to skeptics, if you rewrite all the fractions correctly with horizontal fraction bars, instead of using sloppy slashes. Since I'm too frackin lazy to figure out how to do that in HTML, I'll leave that typographical correction to the reader

Let's begin with the obvious fact:
¹⁄_∞ = 0
Rotate both sides counter-clockwise by a quarter turn:
-18 = 0
Now add 10 to both sides:
-8 = 10
Multiply both sides by -1:
8 = -10
Finally, of course, we must rotate both sides clockwise by a quarter turn:
∞ = ¹⁄₀
QED

[pokerfan]

21. Well then

If 1⁄∞ = 0
then 1⁄0 = ∞ :P

P.S.
16⁄64 = 16⁄64 = 1⁄4

[struggle4progress]

22. Here's another handy way to simplify fractions:

³⁸⁄₅₇
= ⁽³⁺⁸⁾⁄₍₅₊₇₎
= ¹¹⁄₁₂
= ⁽¹⁺¹⁾⁄₍₁₊₂₎
= ²⁄₃

Since people often don't understand from just one example:

⁵⁶⁄₁₄₀
= ⁽⁵⁺⁶⁾⁄_(1+4+0)
= ¹¹⁄₅
= ⁽¹⁺¹⁾⁄₅
= ²⁄₅

[krispos42]

24. Nice try...

³⁴/₅₁

=⁽³⁺⁴⁾/₍₅₊₁₎

≠⁷/₆


:P

[struggle4progress]

37. Well, it works for me:

⁶³⁄₂₁
= ^{(6 + 3)}⁄_{(2 + 1)}
= ⁹⁄₃ (= 3)

⁴⁷⁄₉₄
= ^{(4 + 7)}⁄_{(9 + 4)}
= ¹¹⁄₁₃
= ^{(1 + 1)}⁄_{(1 + 3)}
= ²⁄₄ (= ¹⁄₂)

¹⁴⁸⁄₁₁₁
= ^{(1 + 4 + 8)}⁄_{(1 + 1 + 1)}
= ¹³⁄₃
= ^{(1 + 3)}⁄₃
= ⁴⁄₃

See? Maybe you just need to plan your experiments more carefully

[peruban]

32. Ok, it's not funny anymore.

You're using fancy parlor tricks, I hope people get the joke.

[struggle4progress]

38. Okay, in the interest of full disclosure, I say you can only count on my handy shortcut

if the fraction has the form ^{(9x + r)}?_{(9y + s)} where: (1) r and s are single digit integers and (2) the integers x and y are chosen so that xs = yr

[peruban]

39. I was a mathematics major and tutored my way through college.

But I still don't see what you're getting at. The fraction is an expression, not an equation so there's no solution. Plus, I worked it out on paper and couldn't do much with it. Algebraic manipulation got me this form of the expression:

(9x/(9y+s))+(r/(9y+s))

xs = yr doesn't seem to play a role here as I can't match it up in any form. I don't see a way to cancel or factor anything out.

Now if we had an equation we could solve this puppy but as an expression there's no solution since we're not equating relations with expressions.

So give it to me straight, what's the lowdown on this one?

[struggle4progress]

40. "Casting out nines" is a way of computing the remainder a number leaves when diivided by nine:

the method consists of repeatedly summing the digits until only one digit remains

In other words, if one starts with the decimal expansion of a number of the form 9x + r where r is a single (nonzero) digit, repeatedly summing the digits will produce r. Example: 9*17 + 6 = 159 leads to the sum 1 + 5 + 9 = 15, which leads to the sum 1 + 5 = 6. So suppose a fraction reduces to an equal fraction by repeatedly summing the digits in the numerator and in the denominator. This means that (9x + r)/(9y + s) = r/s. Cross-multiplying and simplifying gives xs = ry

Any easy way to generate examples is to pick digits r, d, s and set (say) x = rd, y = ds. Then xs = ry and it only remains to compute the numerator 9x + r and denominator 9y + s

[peruban]

46. I didn't realize you were using the xs=yr equation to produce an equation.

I worked it out and got the right result, I just didn't realize xs=rs was the final answer, not just algebraic manipulation. I tried factoring, multiplying the numerator and denominator by fractions of one like r/r or s/s. I even tried to distribute that pig into finding things to cancel out. You didn't give the full equation at first with the r/s on the other side of the equation.

After that cross multiplying and canceling out like term the answer was staring me in the face.

Thank you very much for the challenge and please feel free to pm me with any other goodies you may have up your sleeve.

Cheers.

[peruban]

31. That's pretty funny.

I just hope you don't confuse people who don't get the joke.

[Rabrrrrrr]

45. That's awesome! I wish I'd known that in calculus...

:rofl:

"Rotate a quarter-turn counter-clockwise"

Brilliant!

:rofl:

[peruban]

42. The simplest way to explain the zero denominator

is to think of the fraction cutting up an apple into pieces. In this case, the apple slices represent the denominator and taking away slices creates the numerator. Ok, so that analogy sucked but try this one:

The denominator is a defined number that can be broken into parts to create ratios. Since the denominator must be defined as a number that can be divided, zero is called "undefined" because you can't break nothing into something. You can't cut a zero in half or create any ratios with it.

QED

[Jamastiene]

26. Division by 0 is undefined.

When x approached 0, 0 kicked x's ass for claiming that "infinity" measurement. 0 don't take no shit. :P

[peruban]

29. Also Infinity isn't a number, it's an abstract concept.

It's useful in calculus, though, because it describes rates of change.

[onlyadream]

35. you're talking limits

from what I remember from my college days. As you approach zero (if in the denominator) then you approach infinity. But just dividing by zero is undefined.

[surrealAmerican]

61. ... so, it's a question of knowing your limits?

[NoGOPZone]

67. what if x is approaching zero

from the negative side?

1/-0.00000000000000000001 = -100,000,000,000,000,000,000.

As x gets closer and closer to 0, 1/x gets closer to negative infinity.

So division by zero yields negative infinity.

[pokerfan]

15. If you've never seen that

then you probably haven't seen this one:

[JVS]

25. The version I saw was Evil, not Problems

[peruban]

33. Cute, but more bad algebra.

You forgot to square BOTH sides of equation number 5.

[pokerfan]

62. Step five was a substitution

not squaring both sides.

[peruban]

36. Cute but more bad algebra.

Am I the only one here who remembers their algebra?

The "proof" would go like this:

Time and Money define an additive relation, not a multiplicative one. If it was said Time BY money we have multiplication.

So: Woman = Time + Money
Since Time = Money, Woman = 2 Time = 2 Money

Let's stick the money.

Woman = 2 Money

Money being the root of all evil implies that

Problems^2 = Money
Women = (Problems)^1/2
Woman^2 = Problems

QED

The joke looses it's humor when you apply strict algebra.

[Jamastiene]

41. That is the entire point of the joke.

That algebra is wrong, but the teacher liked what the student was saying. :)

[peruban]

47. Like I said, it's cute.

But as a mathematics student seeing so many errors is like nails on a chalkboard.

I do think it's funny, though, and I will be showing my friends this one. I'm not devoid of a sense of humor, you know.

[Jamastiene]

48. I understand that errors can really get on our nerves sometimes.

I tend to get irritated when someone says lighting never strikes the same place twice. Why that myth is continually repeated is beyond me.

Nowadays, I just reply: Uh, lightning attractors and lightning rods...aka Franklin rods... :eyes:

I understand. :pals:
:P

[PVnRT]

51. Only if "and" means to multiply

Otherwise, woman is the square root of 2*PROBLEMS, which isn't really that funny.

[pokerfan]

64. Seems reasonable

the only thing left to determine is whether it's a dot product or a cross product.

I'm going to have to go with cross.

[PVnRT]

65. And women are complicated, so that would involve tensors

[peruban]

27. You're right on some point but not on others.

I looked at it and saw the 0 denominator. Zeros can't be denominators because you can't divide nothing into something.
Also, line 4 is a false equation, if you simplify it it becomes x=2y.
Additionally (x+y)=y is only true when x=0
The first three equations are valid as long x=y=1.
Lines 4 and 5 are just bad algebra and use classic fallacies any basic algebraist would recognize. You could say that it's bad mathematical grammar.

[peruban]

34. I made some mistakes in my first post but this one has them corrected.

I looked at it and saw the 0 denominator in equation 5. Zeros can't be denominators because you can't divide nothing into something. That's the meaning of "undefined" in algebra, the part to be divided has not been defined to be a number.

Additionally, in line 4 when simplified x^2-y^2 = xy-y^2, which is only true whenever x=y=1

In fact, the first four equations are valid as long x=y=1.

Line 5 is just bad algebra and uses a classic fallacy any basic algebraist would recognize. You could say that it's bad mathematical grammar since you can't break a 0 into parts like I said before.

In college a professor showed us a similar problem.

[PVnRT]

49. It all starts with the assumption of x=y, so it really proves nothing

And, yeah, you can't divide by zero, unless you're taking a limit.

[Dr. Strange]

53. Zero, in fact, does equal one.

In fact, all of the positive integers are equal, i.e. if x and y are positive integers, then x = y. You can prove this using induction on n = max{x,y}.
The basis step is easy: If x and y are positive integers whose maximum is 1, then clearly x = y.
The induction step is only somewhat challenging: Suppose that for any two positive integers x and y, if max{x,y} ≤ n, then x = y. Now suppose that x and y are positive integers with max{x,y} ≤ n + 1. Then max{x - 1,y - 1} ≤ n which, by the induction hypothesis, implies that x - 1 = y - 1 and hence x = y.

[TZ]

55. This is a very helpful thread...

All the math geeks have outed themselves!!! Or as DuStrange would put it..all the "math studs".....:rofl:

[motely36]

56. I remember doing that in school

[briv1016]

57. Besides dividing by 0, lines 3 and 4 are wrong in and of themselves.

[Dr. Strange]

58. I don't think so.

In line 3, you're just subtracting y² from both sides. And in line 4, you're just factoring.

[briv1016]

60. No, your right.

I forgot x=y

[Mutley]

59. This thread hurts my brain.

Just thought I'd throw that out there.