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Posers and Puzzles

Posers and Puzzles

  1. Standard member Chorney
    Dan
    14 Jan '04 12:32
    PROOF 2=1!?

    STEP 1: Let a equal b. STEP 2: Multiply each side of the equation by a.
    STEP 3: Add a2 to each side of the equation.
    STEP 4: Subtract 2ab from each side of the equation.
    STEP 5: Factor each side of the equation.
    STEP 6: Divide each side of the equation by (a-b)
    STEP 7: Simplify (2=1)

    Do this equation and see if you can figure out how it is wrong.

    Dan

  2. Standard member royalchicken
    CHAOS GHOST!!!
    14 Jan '04 13:16
    Originally posted by Chorney
    PROOF 2=1!?

    STEP 1: Let a equal b. STEP 2: Multiply each side of the equation by a.
    STEP 3: Add a2 to each side of the equation.
    STEP 4: Subtract 2ab from each side of the equation.
    STEP 5: Factor each side of the equation.
    STEP 6: Divide each side of the equation by (a-b)
    STEP 7: Simplify (2=1)

    Do this ...[text shortened]... an figure out how it is wrong.

    Dan

    You can't divide by a-b, as it is 0.
  3. 14 Jan '04 13:30
    Originally posted by royalchicken
    You can't divide by a-b, as it is 0.
    Of course you can; he just did It is the big equalizer.
  4. Standard member TheMaster37
    Kupikupopo!
    14 Jan '04 15:10
    A shot summary of what happens:

    0*5 = 0*6
    so 5=6

    Clearly everyone sees what's wrong with dividing by 0 now
  5. Standard member Fiathahel
    Artist in Drawing
    03 Feb '04 19:15
    Originally posted by TheMaster37
    A shot summary of what happens:

    0*5 = 0*6
    so 5=6

    Clearly everyone sees what's wrong with dividing by 0 now
    Oh, your so smart. You just screw up all math theories.
    You enormous Kupikupopo!
  6. Standard member flexmore
    Quack Quack Quack !
    04 Feb '04 02:39 / 1 edit
    you can, you can't, you can, you can't you can, you can't, you can, you can't you can, you can't, you can, you can't you can, you can't, you can, you can't you can, you can't, you can, you can't you can, you can't, you can, you can't you can, you can't, you can, you can't you can, you can't, you can, you can't.

    it all depends on what you agree to be allowed. if you agree that you can not divide by zero then you get a system that acts like what we often see in everyday life.

    but you can have a system where you divide by zero. unfortunately it ends up a bit toothless though.

    similarly try:
    infinity+1 = infinity +2
    subtract infinity from both sides
    and 1=2
  7. 07 Feb '04 02:54
    Originally posted by flexmore

    similarly try:
    infinity+1 = infinity +2
    subtract infinity from both sides
    and 1=2
    subtracting infinity and dividing by zero render the result meaningless.
    here's another idea of what happens when you violate the laws of mathematics:
    solve sqrt(4x - x^2) = -2.
    when you get done, you end up with nonsense!
    yours to figure out why.
  8. Standard member Fiathahel
    Artist in Drawing
    07 Feb '04 13:59
    Originally posted by flexmore

    similarly try:
    infinity+1 = infinity +2
    subtract infinity from both sides
    and 1=2
    Apparently you never learned the definitions of infinity. That's the problem with today's education. They don't explain things, they just say it is. That way you only know how to solve things the way you've learned and cannot reason how things should be in a different situation. If they tought you that infinity aint an element of the reals, and so you can't calculate with it as with reals like if a+b=a+c then b=c is only true if a is a real and not when a is infinity, calculating with infinity would be more easy. Everybody could have been good at mathematics, if the education had been proper.

    [[ I don't know if it is completely true for the entire world, but this is how education is in Holland ]]
  9. 08 Feb '04 16:14 / 1 edit
    Originally posted by Fiathahel
    Apparently you never learned the definitions of infinity. That's the problem with today's education. They don't explain things, they just say it is. [parts omitted]
    Everybody could have been good at mathematics, if the education had b ...[text shortened]... or the entire world, but this is how education is in Holland ]]
    i agree.
    when i was in school (a very long time ago), we were taught first that, first, subtracting 3 from 2 could not be done and, later, division by zero is "undefined". no explanation as to why--just that that was how it was.
    when signed numbers were introduced to us, the first operation became feasible, and things got easier for me since i now knew that there were more numbers than i'd first been taught to believe. but dividing 3 into 5 was just given as "1 with a remainder of 2". when was the lsat time you saw that kind of gobbledygook?! once we were taught decimal conversions this became simple, but i still leave 5/3 just like that.
    eventually, the idea that there were number that could not be represented in fractional form, and that this set was "bigger" than the fractions. hmmmmm.
    later, it was explained that dividing by zero is "infinite" but no "value" was given to that notation. still later, the concept of an infinite number of infinities, each "bigger" than its predecessor, was brought in, and my mind boggled.
    it was not until i got into college, however, that i learned that there were two sets of irrational numbers, how they differed, and so forth.
    in my opinion, teh u. s. education system, which depicts itself as the best in the world, is in pretty sad shape when school students cannot form correct sentences, locate things on a map, or do even the simplest math without using a calculator. heck--when i was in school, we didn't even have calculators--you either did the math in yuor head or wrote it on paper!
    it's a sad reflection on our very expensive education system that we turn out such poor specimens, but i don't know what to do about it.
  10. 20 Feb '04 16:42
    Originally posted by BarefootChessPlayer
    subtracting infinity and dividing by zero render the result meaningless.
    here's another idea of what happens when you violate the laws of mathematics:
    solve sqrt(4x - x^2) = -2.
    when you get done, you end up with nonsense!
    yours to figure out why.
    I don't see why this ends up with nonsense. As far as I can tell x=2 and the other solution to the expression would be sqrt(4x - x^2) = 2. Am I missing something?
  11. Standard member Fiathahel
    Artist in Drawing
    20 Feb '04 19:34
    Originally posted by mikenay
    I don't see why this ends up with nonsense. As far as I can tell x=2 and the other solution to the expression would be sqrt(4x - x^2) = 2. Am I missing something?
    Solution? Solution of what? The question is: for what x holds sqrt(4x-x^2)=-2. The question is not: find an expression that is true for x = 2!

  12. 21 Feb '04 06:34
    i was reading about this guy called daniel appolinari, hes some mathematical genius or something but hes working on something along the lines of

    there are infinity odd numbers there are infinity even numbers
    the total of the odd and even numbers equals all the numbers (all odd + all even = all numbers) anyway basically what he is saying is

    infinity + inifinity = infinity

    however its not as simple as that, im studying degree level mathematics and i dont understand it and this daniel appolinari boy is a mathematical purist and he says that he doesnt truely understand it

    so if anyone can bare any light on this it would be good!
  13. 21 Feb '04 06:42
    oh yeh and for sqrt(4x-x^2)=2
    itsnt it so simple that it results in

    (x-2)^2 ???


  14. Standard member flexmore
    Quack Quack Quack !
    21 Feb '04 07:10 / 3 edits
    Originally posted by Fiathahel
    Apparently you never learned the definitions of infinity. That's the problem with today's education. They don't explain things, they just say it is. That way you only know how to solve things the way you've learned and cannot reason h ...[text shortened]... or the entire world, but this is how education is in Holland ]]
    in simple arithmetic you must obey those rules for schoolkids.

    when you grow up you are allowed to mess around a little more and have fun.


    my personal favourite is to take two piles of sand, now apply the addition operation to these piles - and you have a pile of sand !! 1+1=1
  15. Standard member flexmore
    Quack Quack Quack !
    21 Feb '04 07:55
    Originally posted by danthechessman
    i was reading about this guy called daniel appolinari, hes some mathematical genius or something but hes working on something along the lines of

    there are infinity odd numbers there are infinity even numbers
    the total of the odd and even numbers equals all the numbers (all odd + all even = all numbers) anyway basically what he is saying is

    inf ...[text shortened]... that he doesnt truely understand it

    so if anyone can bare any light on this it would be good!
    sounds like he is talking about about comparing the sizes of things.

    let E = size of the set of all even integers
    O = size of the odd integers
    I = size of the set of all integers.

    if we can connect each element in one set to exactly one element in the other set -and cover the whole set - then they are the same size.
    we can do this by simply adding 1 to each even number.

    also the set I is made by simply adding the two sets E and O together, E and O contain no elements the same so obviously E + O = I

    inf + inf = inf

    but this is all very old elementary stuff, so some wizzkid must surely be doing something else. i googled the name, nothing showed up.