Impossible Math Question?

Originally posted by SpookyVince
Kalisdad, NO. It is clear that it is not x + (1/2) x = x.

OP says 'If not number, then maybe what element + half of itself would = itself?"

how is this not x+(1/2)x=x?

I never said the variable was or had to be a number

Originally posted by Wildmanimal
reply to post by billb1215

 

By The way,,,Dyson,Oreck,and Electrolux have made a fortune with this concept.

You forgot the government;

Originally posted by demonseed
What number + 1/2 would equal itself again?

(not half of itself, just 1/2)

Indeed an insteresting questions. However, please list your assumptions

Using the basic assumptions this is impossible.
X+1/2 = X
resolves itself to 1/2 = 0.

So are you asking for what operation is 1/2 an identity? How do you define "+" then is the real question.
"+" is just a rule, and in different algebras could mean ... well, anything.. not just what we assume in our every day life.

Also another assumption is, what number set are we working in? Our operators and theorems do not always hold solid outside the real number system.
Consider:
1 = Sqroot(1) = Sqroot( -1 * -1) = Sqroot(-1) * sqroot(-1) = i* i = i^2 = -1
And by this 1 = -1
which again is impossible.
However using the princples of the complex number system, the rules are different and there is a step here that cannot be done due to continuity.

Also consider radians, is there something like Sin(x) + 1/2 = sin(y)? Where sin(x) = sin(y)

like in radians: sin(0) + 2pi = sin(2pi).. 0, 2pi, 4pi.. etc all really the same point on the unit circle

Here is another fun "impossiblility"

e^(i*pi) + 1 = 0

It is on the tombstone of the famous mathematician Leonard Euler...

This example and the 1=-1 one were primary reasons why mathematicians in Euler's time called them imaginary numbers... hence, the "i".
Engineers call this value "j"

But again, using operators on a number system for numbers that may not be in that set can lead to false results.

It sounds to me, that you are simply looking for a cycle that repeats itself. We this this happen all the time. 1/3 of anything is .33 repeated. I don't think its possible to do this with 1/2, because half of something will always be half of something, it can't equal itself over again, but 1/3 can.

as I said on pg one:

half life — symbol t1/2 — the time taken for the activity of a given amount of a radioactive substance to decay to half of its initial value.

en.wikipedia.org...

Would someone please explain to me why this doesn't satisfy the requirements as stated?

a mass of radioactive element plus half its mass equals itself...eventually
every math question on every math test any where in the known universe takes time to solve
since the time factor in this case is open ended case closed.

reply to post by Danbones


half life function on exponential decay and I believe needs differential equations to solve, which on the face of it is not our standard and abilian concept of the operator +.

Again, what is + in all this? Assumptions have to be stated.

Originally posted by SpookyVince
Kalisdad, NO. It is clear that it is not x + (1/2) x = x.

Now there's something.

Adding doesn't necessarily means "to perform the mathematical addition".

So: instead of "additioning" let's simply "add" (collate, stick to) 1/2 to 2/4. This needs to be seen with horizontal fraction bars:
2 1
- -
4 2

That would be 2/4 "+" 1/2 -> 21/42 wich is still 1/2.

or
1+2=3
-- -- ---
2+4=6

Originally posted by catlantis
reply to post by Danbones

 

half life function on exponential decay and I believe needs differential equations to solve, which on the face of it is not our standard and abilian concept of the operator +.

Again, what is + in all this? Assumptions have to be stated.

I'm not sure, but I think the OP is trying to get us to design an overunity device for him.

reply to post by catlantis


the mass + one half mass equals half it self needs no "anything" except time to complete
sorry
I said prove

hey dave
you could be right

I am not going to share my over unity device unless he asks nicely...
how ever I will share the secret to the 11 herbs and spices
if he offers to send me a six pac of Heineken

as a bonus I will even share with him a magic phrase
that will make certain physical things appear on a table
seemingly out of no where

1 gallon cylinder with 1 gallon compressed gas inside +
1/2 gallon compressed gas = 1 gallon compressed gas

VO2+½= VO2???

reply to post by Danbones


Ah, so you assume time in this. Did the op?

Is the mass of the substance A at t1 = mass of the substance A at t2, where t1 = initial and t2 is the time of the half life?

The mass should have decayed into either energy or some other substance.
The total mass and energy of the system (if truly closed) should, remain constant over the time.

How about this one:
Three guys rent a motel room for $30.00 . Thinking they paid too much, the desk clerk gives the bellhop $5.00 to give back to the three guys. Instead the bellhop decides to keep $2.00 for himself, and gives the guys back $3.00 . So now instead of paying $10.00 for the room, each has now paid $9.00 .
3 X $9.00 = $27.00 + $2.00 the bellhop kept = $29.00 . Where is the other $1.00 ?

reply to post by Bkrmn


I hate this riddle IT made me feel really stupid the first time I tried to work it out

reply to post by Bkrmn


It's not 27 dollars, when you subtract 2 dollars from 30 you get 28 dollars. The three guys paid 9.33 each. 33+33+33= the one dollar that is missing.

The remaining dollar, lies with the desk clerk.

Originally posted by Bkrmn
How about this one:
Three guys rent a motel room for $30.00 . Thinking they paid too much, the desk clerk gives the bellhop $5.00 to give back to the three guys. Instead the bellhop decides to keep $2.00 for himself, and gives the guys back $3.00 . So now instead of paying $10.00 for the room, each has now paid $9.00 .
3 X $9.00 = $27.00 + $2.00 the bellhop kept = $29.00 . Where is the other $1.00 ?

there is no missing money

in the end they paid $25 for the room plus the $3 they got back, plus $2 that the bellhop kept

that is the original $30

from the renters perspective, they paid $27 or $9 each, but when you subtract the $2 from that you get the $25 they actually paid for the room


in reality they only paid $8.33 each for the room,but the bellhop stole an extra $0.667 from each of them... being the $2 he pocketed

reply to post by xxshadowfaxx


close, but we know they didn't pay $9.33 each, the room only cost $25

this is the first time I have heard this riddle... you need to take into account the actual numbers, not the percieved numbers

Looking at this a different way (pun intended) what about your reflection in a mirror?
Or anything reflected in a mirror?