An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers. ”
— Randgruppenhumor cont’d
Explanation of this joke to those of you that do not understand:
The first mathematician orders a full beer, the second orders a half, the third orders a quarter, the forth orders an eighth. Theoretically what they are doing here is splitting the unfilled portion of the cup in halves and “filling” it, then repeating the step with the remaining unfilled portion. The bartender understands that even with an infinite amount of splitting in half and filling that cup will never ever reach 100% full because its always going up by half of whats left to fill even if poured infinite times. So therefore he just gives them 2 full beers which would be the easy way out of the problem, but also an incorrect outcome. It will go to an infinite amount of decimal places and never reach 100% capacity.
The reason it is a joke is because the sum of all their beers will never be two beers. Infinity is not a real number and has a sequence of continuation that never ends.
1 + Σ(1/2^n) = 2
Side Tracking:
Obviously this scenario is not possible due to the fact that it assumes you can split beer infinitely which you CANNOT. Once you are at the molecular stage you are done. If you split a beer molecule you no longer have beer.
http://www.maurysart.com/main.php?g2_itemId=195
Another reason why this scenario is not possible is because you will need an infinite number of mathematicians, which just isn’t possible. Just enjoy the joke and stop trying to think why it is not possible. We know it is not possible, we just want to enjoy the theory behind it. Thanks!
Sorry for any confusion, but infinity as a mathematical concept is not necessarily what you heard as a five year old. As a five year old, you probably just thought of it as the biggest possible number, but mathematically, infinity is never reached.
The best you can do is to talk about outcomes as a number “approaches” infinity.
For example, 1 / ∞ = 0 is a simplistic way of noting that the larger the denominator in this equation, the closer the number will be to zero. But mathematically speaking, no matter how large the number is, the result will be greater than zero.
That is why we understand infinity using the concepts of limits. You can accurately say of the above equation that as the denominator approaches infinity, the result approaches zero from above.
From above just means that it is always greater than zero. In the original question (about 2 beers), you are approaching from below.
Another example is the Leibniz formula for pi
http://en.wikipedia.org/wiki/Leibniz_formula_for_p …It is an infinite series that after an infinite number of expressions will exactly represent pi/4. As you can never technically get to infinity, you can say that this series approaches pi/4, but it converges on pi/4 from both above and below.
PS: Yes, all numbers are concepts, but they are concepts representing tangible things. Infinity is a concept of a number, just like ‘i’ (√-1). It is something that may be helpful to describe concepts, but not a real number.
p.s. I know I am a geek and I embrace it!
Want more jokes?
The bartender pours the second-to-last atom of beer, then they split the last atom of beer and the whole bar explodes (splitting atoms can be a bad thing, U235 example).
Now for an actual joke:
A biologist, a physicist, and a mathematician are eating lunch at a patio cafe. All three of them observe 2 persons enter a building across the street. A few moments later, three persons exit the same building.
The biologist postulates that they reproduced and the third person was their offspring.
The physicist thinks that one slapped the other so hard that he/she split bringing their total to three.
The mathematician simply says that there are now negative one people in that building.