Dragonfall said:
METHODS FOR PUTTING AN ELEPHANT INTO A REFRIGERATOR:
Algebra: Show that parts of the elephant can be put into the fridge, then show that the fridge is closed under addition.
Number Theory: Use induction, you can always squeeze a bit more in.
Analysis: Differentiate the elephant, put it inside the fridge, then integrate.
Topology: The elephant is compact, so it can be put into a finite collection of refrigerators. That's usually good enough.
Algebraic topology: Replace the interior of the refrigerator by its universal cover, R^3.
Set theory: refrigerator = { elephant }
Numerical analysis: Put its trunk in and refer the rest to the error term.
Analysis:
1) Differentiate it and put into the refrig. Then integrate it in the refrig.
2) Redefine the measure on the referigerator (or the elephant).
3) Apply the Banach-Tarski theorem.Number theory:
1) First factorize, second multiply.
2) Use induction. You can always squeeze a bit more in.
Algebra:
1) Step 1. Show that the parts of it can be put into the refrig.
Step 2. Show that the refrig. is closed under the addition.
2) Take the appropriate universal refrigerator and get a surjection from refrigerator to elephant.
Topology:
1) Have it swallow the refrig. and turn inside out.
2) Make a refrig. with the Klein bottle.
3) The elephant is homeomorphic to a smaller elephant.
4) The elephant is compact, so it can be put into a finite collection of refrigerators. That's usually good enough.
5) The property of being inside the referigerator is hereditary. So, take the elephant's mother, cremate it, and show that the ashes fit inside the refrigerator.
6) For those who object to method 3 because it's cruel to animals. Put the elephant's BABY in the refrigerator.
Algebraic topology:
Replace the interior of the refrigerator by its universal cover, R^3.
Linear algebra:
1) Put just its basis and span it in the refrig.
2) Show that 1% of the elephant will fit inside the refrigerator. By linearity, x% will fit for any x.
Affine geometry:
There is an affine transformation putting the elephant into the refrigerator.
Set theory:
1) It's very easy!
refrigerator = { elephant }
2) The elephant and the interior of the refrigerator both have cardinality c.
Geometry:
Declare the following:
Axiom 1. An elephant can be put into a refrigerator.
Complex analysis:
Put the refrig. at the origin and the elephant outside the unit circle. Then get the image under the inversion.
Numerical analysis:
1) Put just its trunk and refer the rest to the error term.
2) Work it out using the Pentium.
Statistics:
1) bright statistician.
Put its tail as a sample and say "Done."
2) dull statistician.
Repeat the experiment pushing the elephant to the refrig.
3) Our NEW study shows that you CAN'T put the elephant in the refrigerator.