Terms and technicalities...
Mokkies asked me..what's a lemma. Well to satisfy you and to give my readers a little insight into mathematical mumbo jumbo (which it is not) I shall try to explain the what words "Theorem", "Proposition", " Lemma" and "Corollary" means.
Theorem: All the four words above mean this: True assertions. Thus, in a way of speaking, theorem=proposition=lemma=corollary. But this does not mean they can be used interchangably. Confused?
:P
Proposition: A theorem is used to state an interesting result, a major fact or (strong) assertion. It sets up the theme and direction of the discussion. In other words, Theorems are the big picture statements.
Propositions on the other hand are results that tend to be technical in nature. You can compare them to the nuts and bolts of the engine.
Lemma's are vignettes. Small results proved on the way to make life easier (and possible). They are 'little theorems' so to speak; like the oil of the engine.
A corollary simply means a direct consequence. For example: The p-series diverges for s=1. A corrollary to that would be that there are infinitely many primes.
Boleh? Faham? Understand?
Lemma: All four of the above require proofs.
Corollary: If you see of such words and the space below them is blank, the perogative on you as the reader is to try to prove those assertions.
Perhaps the interesting question to test whether you have understood me is this.
Theorem: All the four words above mean this: True assertions. Thus, in a way of speaking, theorem=proposition=lemma=corollary. But this does not mean they can be used interchangably. Confused?
:P
Proposition: A theorem is used to state an interesting result, a major fact or (strong) assertion. It sets up the theme and direction of the discussion. In other words, Theorems are the big picture statements.
Propositions on the other hand are results that tend to be technical in nature. You can compare them to the nuts and bolts of the engine.
Lemma's are vignettes. Small results proved on the way to make life easier (and possible). They are 'little theorems' so to speak; like the oil of the engine.
A corollary simply means a direct consequence. For example: The p-series diverges for s=1. A corrollary to that would be that there are infinitely many primes.
Boleh? Faham? Understand?
Lemma: All four of the above require proofs.
Corollary: If you see of such words and the space below them is blank, the perogative on you as the reader is to try to prove those assertions.
Perhaps the interesting question to test whether you have understood me is this.
Have I used the words properly when I boldfaced them as section headings?
This entry was posted
on Tuesday, September 06, 2005 at 9:38 PM.
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11:52 PMdot...dot...dot...
guess some of us aren't cut out for the whole lemma thing, hahaha...
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