X=Y
X-Y = 0
2X-2Y=0
X-Y = 2X-2Y
1(X-Y) = 2(X-Y)
1 = 2
X-Y = 0
2X-2Y=0
X-Y = 2X-2Y
1(X-Y) = 2(X-Y)
1 = 2
Math Mystery
Miscellaneous Forums/General Discussion/Math Mystery Indeed.
1(X-Y) = 2(X-Y)
u lost me right there....i suck at math...never liked it...never want it....
1 = 2?
? it still doesnt prove that 1 == 2
Half-past badger.
X-Y = 0, and you're dividing by X-Y on the last line - division by 0 ain't allowed!
Yeah and if you use substitution instead:
X-Y = 0
1(X-Y) = 2(X-Y)
1*0 = 2*0
0 = 0
X-Y = 0
1(X-Y) = 2(X-Y)
1*0 = 2*0
0 = 0
This line is the leap of logic: 1(X-Y) = 2(X-Y) because if X and Y are 0, then it's 0 = 0 as sswift said.
1 == 2 for values of 0 not equal to 0.
I can't believe this is being discussed.
It's plain wrong :-)
It's plain wrong :-)
42
1 = 2
That's a contradiction, your argument is invalid.
X and Y both equal zero.
As Ryan Moody said - division by zero is a big no no
Thank you :)
yup - 42
I see what you mean, nawi. The same thing could be done with any equasion:
e = mc^2
0 = mc^2-e {subtract e from each side}
3*0 = 3mc^2-3e {multiply 3x each side}
0 = 3mc^2-3e {3*0 is 0}
mc^2-e = 3mc^2-3e {substituting 0 for mc^2-e, which is 0}
1(mc^2-e) = 3(mc^2-e) {factor}
1 = 3 {dividing by mc^2-e}
...
What??? :)
As Ryan Moody said, the problem is when you divide both sides by (X-Y), or 0.
In your example, this:
Is true provided that X=Y, as stated above.
Now, when you derive the 1=2 by removing the (X-Y), you are forgetting that you may divide both sides of an equasion by any number other than zero. Since (X-Y) = 0, you can't do this.
The reason things like this don't occur very often (for me, at least) is that when I see something like "X = Y", I immediately substitute. For example, this:
Immediately becomes this:
.. when you know that Y=X.
e = mc^2
0 = mc^2-e {subtract e from each side}
3*0 = 3mc^2-3e {multiply 3x each side}
0 = 3mc^2-3e {3*0 is 0}
mc^2-e = 3mc^2-3e {substituting 0 for mc^2-e, which is 0}
1(mc^2-e) = 3(mc^2-e) {factor}
1 = 3 {dividing by mc^2-e}
...
What??? :)
As Ryan Moody said, the problem is when you divide both sides by (X-Y), or 0.
In your example, this:
1(X-Y) = 2(X-Y)
Is true provided that X=Y, as stated above.
Now, when you derive the 1=2 by removing the (X-Y), you are forgetting that you may divide both sides of an equasion by any number other than zero. Since (X-Y) = 0, you can't do this.
The reason things like this don't occur very often (for me, at least) is that when I see something like "X = Y", I immediately substitute. For example, this:
X-Y = 2X-2Y
Immediately becomes this:
X-X = 2X-2X
or
0 = 0
or
0 = 0
.. when you know that Y=X.
where does nawi state that both x and y = 0? It says x=y; so x-y=0 is true but x=0 and y=0 is not always true.
Octo nailed it in his post
Octo nailed it in his post
[edit] oops
.99999999 = p
p = 9.99999999999
9p - p = 8
8p = 9
p =1
0.9999 = 1
p = 9.99999999999
9p - p = 8
8p = 9
p =1
0.9999 = 1
Dont blame me this is quoted from a mate.
K = 1/3
k = 0.3333333
3k = 1 '3*(1/3) = 1
0.99999 = 1
k = 0.3333333
3k = 1 '3*(1/3) = 1
0.99999 = 1
oh and...
if theres 5 apples on the wall and u eat one .
theres one less apple on the wall
Now it's my turn!!
5 = 3
1 = 8888
999.54 = 13
I love those math mysteries! 1 = 8888
999.54 = 13
If theres 5 apples on the wall and u eat one .
theres one less apple on the wall
Thanks, Einstein! :P theres one less apple on the wall
K = 1/3
k = 0.3333333
3k = 1 '3*(1/3) = 1
0.99999 = 1
A number can infact have 2 decimal expansions - I believe 1.00000... and 0.99999.... are equivalent.
Edit: Yes, they are equivalent.
WOW! They've legalized marihuana.
Ryan... they are not.. they are NEAR equivalent.
No, 1.0 is equivelent to .9999999->infinitive number of nines.
but .99999 is exactly .00001 less than 1.0
Note this line in the .pdf you posted
but .99999 is exactly .00001 less than 1.0
Note this line in the .pdf you posted
Theorem. The only equivalences generated in this way are from infinite strings of nines.
Puki made the most sens tbh
the proper representation of .3333... is 1/3. .333... is not precise and because it can't truely represent what 1/3 is, it isn't accurate enough to be used litterally.
Take Pi, for example, Pi can't be represented in either decimal or fractional notation, yet it can be measured in application, it doesn't have a rational number associated with it because it isn't a rational number.
Whomever proposed this theory is working on the assumption that infinity is rational and obey's traditional laws of addition. It does not, .3333... times 3 = 1.
Take Pi, for example, Pi can't be represented in either decimal or fractional notation, yet it can be measured in application, it doesn't have a rational number associated with it because it isn't a rational number.
Whomever proposed this theory is working on the assumption that infinity is rational and obey's traditional laws of addition. It does not, .3333... times 3 = 1.
Actually the proper representation of .33333... is
_
.3
That is, the 3 with a line over it which represents that the pattern is to be repeated to infinity and is equal to 1/3.
Most people on computers will use "..." when overstrikes are not available.
http://www.intermath-uga.gatech.edu/tweb/gwin1-01/apley/Dictionary/Fractions/TMP-1115484092.htm#anchor1519067
http://www.academicmeet.com/tricks/repeating_decimals.pdf
_
.3
That is, the 3 with a line over it which represents that the pattern is to be repeated to infinity and is equal to 1/3.
Most people on computers will use "..." when overstrikes are not available.
http://www.intermath-uga.gatech.edu/tweb/gwin1-01/apley/Dictionary/Fractions/TMP-1115484092.htm#anchor1519067
http://www.academicmeet.com/tricks/repeating_decimals.pdf
Correct Tom, I use ... for .3 with a line over the 3.
Infinity is an imaginary number like i is. The use of it doesn't follow traditional math logic.
Infinity is an imaginary number like i is. The use of it doesn't follow traditional math logic.
this topic is insane :P
1 != 2
the only way to find that equality is removing the whole brackets mentioned below, but does not mathematically correct!
1(X-Y) = 2(X-Y)
and just try to replace any number for x and y and you will find your solution is not consistent!
B!
1 != 2
the only way to find that equality is removing the whole brackets mentioned below, but does not mathematically correct!
1(X-Y) = 2(X-Y)
and just try to replace any number for x and y and you will find your solution is not consistent!
B!
Quote from the maths PDF:
GobbledegookGobbledegookGobbledegook. Gobbledegook Gobbledegook. GobbledegookGobbledegookGobbledegook, GobbledegookGobbledegookGobbledegookGobbledegook. Whatsitwhowhen....
Well, Thats self explanitory!
GobbledegookGobbledegookGobbledegook. Gobbledegook Gobbledegook. GobbledegookGobbledegookGobbledegook, GobbledegookGobbledegookGobbledegookGobbledegook. Whatsitwhowhen....
Well, Thats self explanitory!
MAV
i am sorry I am the culprit who dug this up again, Stevie G said he used to use repeat until 1=2 instead of forever in another forum and i couldnt resist. Very confusing topic
Obviously a quiet day on the coding front:D
*nods his head in agreement*
How about this one (It makes more sense when I tell it as a story... sorry!):-
Three flatmates are walking down the street, they pass an electrical shop and see a 32 inch plasma screen for £15, interested, they enter the shop and see if the offer is'nt a mistake!
Sure enough, the shop assistant says it's correct and the three flatmates dig into their pockets and they have £5 each, so they buy it.
As they are walking out of the shop with their plasma TV, the manager enters and says to the shop assistant "I see you managed to sell that TV, how much did you get for it?", "£15" replied the assistant.
"Well I really only wanted £10 for it, go and give them a £5 back" said the manager.
So the shop assistant takes 5 pound coins and runs after the flatmates.
After he catches up with them, he says he's overcharged them and gives them 3 pound coins and keeps 2 for himself...
That means the three flatmates have only payed £4 each, which is £12, the shop assistant only kept £2, that's £14...
Where's the £1 gone??? :)
Dabz
Three flatmates are walking down the street, they pass an electrical shop and see a 32 inch plasma screen for £15, interested, they enter the shop and see if the offer is'nt a mistake!
Sure enough, the shop assistant says it's correct and the three flatmates dig into their pockets and they have £5 each, so they buy it.
As they are walking out of the shop with their plasma TV, the manager enters and says to the shop assistant "I see you managed to sell that TV, how much did you get for it?", "£15" replied the assistant.
"Well I really only wanted £10 for it, go and give them a £5 back" said the manager.
So the shop assistant takes 5 pound coins and runs after the flatmates.
After he catches up with them, he says he's overcharged them and gives them 3 pound coins and keeps 2 for himself...
That means the three flatmates have only payed £4 each, which is £12, the shop assistant only kept £2, that's £14...
Where's the £1 gone??? :)
Dabz
You started with 15 Pounds.
Now the Shopkeeper has 10
the Blokes have 3
and the toady has 2, so it still adds up to 15
I forget what math rule the story breaks when doing it the other way round.
Now the Shopkeeper has 10
the Blokes have 3
and the toady has 2, so it still adds up to 15
I forget what math rule the story breaks when doing it the other way round.
Yeah, it's a strange one! :D
Dabz
Dabz
5 + 5 + 5 = 15
15 - 3 = 12
12 - 2 = 10
adding the 2 to the 12 is backwards. the 2 should be added to the 10.
the boys did pay 12 pounds, 10 to the shop keeper, and 2 to the clerk.
each boy as 1 pound, the clerk 2, and the keeper 10
1 + 1 + 1 + 2 + 10 = 15
Answer is, your math is wrong.
cause you said
boys payed 12, and the clerck kepts 2, well the 2 goes on the other side of the = sign, with the keepers 10
4 + 4 + 4 = 10 + 2
15 - 3 = 12
12 - 2 = 10
adding the 2 to the 12 is backwards. the 2 should be added to the 10.
the boys did pay 12 pounds, 10 to the shop keeper, and 2 to the clerk.
each boy as 1 pound, the clerk 2, and the keeper 10
1 + 1 + 1 + 2 + 10 = 15
Answer is, your math is wrong.
cause you said
boys payed 12, and the clerck kepts 2, well the 2 goes on the other side of the = sign, with the keepers 10
4 + 4 + 4 = 10 + 2
hmmm, I see exactly what your saying Dabz! And I see where its getting confusing, dampes8n is right though:
They only paid a total of 12 for it, 10 went to the shopkeep, and 2 to the troll, they each still have 1 in their pockets.
So as his formula states:
4(flatmate) + 4(flatmate) + 4(flatmate) = 10(shopkeep) + 2(troll)
In your logic, your saying (4x3)+2 = 14 (where the question really is "where did the 2 come from?") If each flatmate only paid 4, there's only 12 to work with total, not 15 anymore.
So to put it in your formula, it should be:
(4(per flatmate) x 3(numMates)) + 3(Given Back) =10(shopkeep) + 2(Troll)+ 3(flatmates have in pocket) = 15
(4x3)+3 = 10+2+3 = 15
They only paid a total of 12 for it, 10 went to the shopkeep, and 2 to the troll, they each still have 1 in their pockets.
So as his formula states:
4(flatmate) + 4(flatmate) + 4(flatmate) = 10(shopkeep) + 2(troll)
In your logic, your saying (4x3)+2 = 14 (where the question really is "where did the 2 come from?") If each flatmate only paid 4, there's only 12 to work with total, not 15 anymore.
So to put it in your formula, it should be:
(4(per flatmate) x 3(numMates)) + 3(Given Back) =10(shopkeep) + 2(Troll)+ 3(flatmates have in pocket) = 15
(4x3)+3 = 10+2+3 = 15
I know there is actually no money missing, but it is a puzzler for people! I've told that story so many times over a beer, and the look on peoples faces is great! :)
Dabz
Dabz
Here's how I figure it:
First, there is:
Buyers: 15
Sellers: 0
After buying the plasma TV (15 from buyer to seller)
Buyers: 0
Sellers: 15
After refund (3 from seller to buyer):
Buyers: 3
Sellers: 12
And, of course, the total is still 15.
Correct.
Correct.
Incorrect.
As Dark Half said, to correctly add up the money, you must add:
3 (refund) + 10 (shopkeeper) + 2 (assistant) = 15.
First, there is:
Buyers: 15
Sellers: 0
After buying the plasma TV (15 from buyer to seller)
Buyers: 0
Sellers: 15
After refund (3 from seller to buyer):
Buyers: 3
Sellers: 12
And, of course, the total is still 15.
That means the three flatmates have only payed £4 each, which is £12,
Correct.
the shop assistant only kept £2,
Correct.
that's £14...
Incorrect.
As Dark Half said, to correctly add up the money, you must add:
3 (refund) + 10 (shopkeeper) + 2 (assistant) = 15.
Yes, I know how it works, if you actually used coins, but having someone think "Okay, they paid 4 pound each because they got refunded £1, that means they paid £12 between them and the troll kept £2, that equals £14?"
People do scratch their heads at this...
lol
Dabz
:)
People do scratch their heads at this...
lol
Dabz
:)
You just set them up to failure because they assume the information you gave them was correct.
When you give out false info, they don't fact check it and start looking for the 1 pound, and they of course can't ever find it.
only other number is a 10, which works out to 24, oddly enough.
24 = 2 * 12.
which happened cause you lumped all the numbers to one side of the equation.
The average person doesn't consider 2 + 10 = 12 as an equation, they consider it a solved problem, so they never attempt to check if it makes any sense.
so when you say 2 + 4 + 4 + 4 = 14 they don't instantly see what is wrong with how you got there. They see a correct solved problem, not an inncorrect evolution of the same problem.
5 + 5 + 5 = 15
5 + 5 + 5 = 10 + 5
4 + 4 + 4 = 12
4 + 4 + 4 + 3 = 12 + 2
when you lay it out like that it makes no sense
5 + 5 + 5 = 15
5 + 5 + 5 = 10 + 5
5 + 5 + 5 - 3= 10 + 5 - 3
4 + 4 + 4 = 10 + 2
telling a lie to people when they aren't equiped to process a lie is just cruelty, it isn't a brain teaser.
its like handing someone 3 toothpicks and asking them to make a perfect square with them, useing 100% of the toothpicks.
Then if they happen to find the 1 way, you tell them that it doesn't look perfect to you, they are all broken and stuff.
When you give out false info, they don't fact check it and start looking for the 1 pound, and they of course can't ever find it.
only other number is a 10, which works out to 24, oddly enough.
24 = 2 * 12.
which happened cause you lumped all the numbers to one side of the equation.
The average person doesn't consider 2 + 10 = 12 as an equation, they consider it a solved problem, so they never attempt to check if it makes any sense.
so when you say 2 + 4 + 4 + 4 = 14 they don't instantly see what is wrong with how you got there. They see a correct solved problem, not an inncorrect evolution of the same problem.
5 + 5 + 5 = 15
5 + 5 + 5 = 10 + 5
4 + 4 + 4 = 12
4 + 4 + 4 + 3 = 12 + 2
when you lay it out like that it makes no sense
5 + 5 + 5 = 15
5 + 5 + 5 = 10 + 5
5 + 5 + 5 - 3= 10 + 5 - 3
4 + 4 + 4 = 10 + 2
telling a lie to people when they aren't equiped to process a lie is just cruelty, it isn't a brain teaser.
its like handing someone 3 toothpicks and asking them to make a perfect square with them, useing 100% of the toothpicks.
Then if they happen to find the 1 way, you tell them that it doesn't look perfect to you, they are all broken and stuff.
telling a lie to people when they aren't equiped to process a lie is just cruelty, it isn't a brain teaser
That's a bit harsh DampeS8N! :(
I say it to people as jest, like many other things people do when they are having a drink.
I once bet a bloke in the pub (who thought he'd seen every trick in the book) that I could make him balance his pint on the end of pool cue. He said it couldnt be done, so I told him to get a pool cue with rubber on the end and stand in the middle of the pub. I grabbed his pint and stood on a chair and placed his drink on top of it... After a couple of 'Are you ready?' (In a serious voice) and 'lift it a bit higher', the pint glass wedged itself between the ceiling and the cue, so I jumped down and moved the chair away and sat back down.
He was stuck, and could'nt go no where! :D
Now, just because he wasnt equiped enough to realise that I was intending to wedge his glass to the ceiling doesnt constitute me as a liar, it constitutes me as a person just having a little fun...
It's the same with that story above...
If people cannot re-evalute the equation on their own because they were too busy taking no notice at school, that also doesnt suggest I'm a liar as well, the numbers are there.
Anyway...
Dabz