How exactly does a lemma differ from another type of proposition (like a theorem or corollary)?
How exactly does a lemma differ from another type of proposition (like a theorem or corollary)?
I think it is that lemmas are used to help prove theorems and coroallary are specific cases of theorems. Is this correct?
terminology
edited Nov 25 at 3:45
Shaun
8,701113680
asked Nov 25 at 3:35
Carlos Bacca
178116
add a comment |
How exactly does a lemma differ from another type of proposition (like a theorem or corollary)?
I think it is that lemmas are used to help prove theorems and coroallary are specific cases of theorems. Is this correct?
terminology
edited Nov 25 at 3:45
Shaun
8,701113680
asked Nov 25 at 3:35
Carlos Bacca
178116
Possible duplicate of Lemma vs. Theorem
– Somos
Nov 25 at 13:39
add a comment |
How exactly does a lemma differ from another type of proposition (like a theorem or corollary)?
I think it is that lemmas are used to help prove theorems and coroallary are specific cases of theorems. Is this correct?
terminology
edited Nov 25 at 3:45
Shaun
8,701113680
asked Nov 25 at 3:35
Carlos Bacca
178116
How exactly does a lemma differ from another type of proposition (like a theorem or corollary)?
I think it is that lemmas are used to help prove theorems and coroallary are specific cases of theorems. Is this correct?
terminology
terminology
edited Nov 25 at 3:45
Shaun
8,701113680
asked Nov 25 at 3:35
Carlos Bacca
178116
edited Nov 25 at 3:45
Shaun
8,701113680
asked Nov 25 at 3:35
Carlos Bacca
178116
edited Nov 25 at 3:45
Shaun
8,701113680
edited Nov 25 at 3:45
Shaun
8,701113680
edited Nov 25 at 3:45
Shaun
8,701113680
8,701113680
asked Nov 25 at 3:35
Carlos Bacca
178116
asked Nov 25 at 3:35
Carlos Bacca
178116
asked Nov 25 at 3:35
Carlos Bacca
178116
178116
Possible duplicate of Lemma vs. Theorem
– Somos
Nov 25 at 13:39
add a comment |
Possible duplicate of Lemma vs. Theorem
– Somos
Nov 25 at 13:39
Possible duplicate of Lemma vs. Theorem
– Somos
Nov 25 at 13:39
Possible duplicate of Lemma vs. Theorem
– Somos
Nov 25 at 13:39
add a comment |
1 Answer
1
active
oldest
votes
There is no formal difference between a "theorem" and "lemma".
As you have noticed, propositions tend to be called "lemmas" when the author's main purpose in proving them is as a stepping stone to proving something more interesting. But ultimately is is subjective what one considers "interesting" enough to be called a theorem.
There are also results that are important enough to have capitalized names and nevertheless are called lemmas, such as for example Zorn's lemma. This is sometimes a pure accident of history, but also sometimes to suggest that whereas the result does not look particularly interesting on its surface, it is a useful component for proving more substantial propositions.
answered Nov 25 at 3:37
Henning Makholm
238k16303537
Le theoreme de Zorn, Zorn's lemma , a bit of history, perhaps of interest.en.m.wikipedia.org/wiki/Zorn%27s_lemma
– Peter Szilas
Nov 25 at 6:57
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
There is no formal difference between a "theorem" and "lemma".
As you have noticed, propositions tend to be called "lemmas" when the author's main purpose in proving them is as a stepping stone to proving something more interesting. But ultimately is is subjective what one considers "interesting" enough to be called a theorem.
There are also results that are important enough to have capitalized names and nevertheless are called lemmas, such as for example Zorn's lemma. This is sometimes a pure accident of history, but also sometimes to suggest that whereas the result does not look particularly interesting on its surface, it is a useful component for proving more substantial propositions.
answered Nov 25 at 3:37
Henning Makholm
238k16303537
Le theoreme de Zorn, Zorn's lemma , a bit of history, perhaps of interest.en.m.wikipedia.org/wiki/Zorn%27s_lemma
– Peter Szilas
Nov 25 at 6:57
add a comment |
There is no formal difference between a "theorem" and "lemma".
As you have noticed, propositions tend to be called "lemmas" when the author's main purpose in proving them is as a stepping stone to proving something more interesting. But ultimately is is subjective what one considers "interesting" enough to be called a theorem.
There are also results that are important enough to have capitalized names and nevertheless are called lemmas, such as for example Zorn's lemma. This is sometimes a pure accident of history, but also sometimes to suggest that whereas the result does not look particularly interesting on its surface, it is a useful component for proving more substantial propositions.
answered Nov 25 at 3:37
Henning Makholm
238k16303537
Le theoreme de Zorn, Zorn's lemma , a bit of history, perhaps of interest.en.m.wikipedia.org/wiki/Zorn%27s_lemma
– Peter Szilas
Nov 25 at 6:57
add a comment |
There is no formal difference between a "theorem" and "lemma".
As you have noticed, propositions tend to be called "lemmas" when the author's main purpose in proving them is as a stepping stone to proving something more interesting. But ultimately is is subjective what one considers "interesting" enough to be called a theorem.
There are also results that are important enough to have capitalized names and nevertheless are called lemmas, such as for example Zorn's lemma. This is sometimes a pure accident of history, but also sometimes to suggest that whereas the result does not look particularly interesting on its surface, it is a useful component for proving more substantial propositions.
answered Nov 25 at 3:37
Henning Makholm
238k16303537
There is no formal difference between a "theorem" and "lemma".
As you have noticed, propositions tend to be called "lemmas" when the author's main purpose in proving them is as a stepping stone to proving something more interesting. But ultimately is is subjective what one considers "interesting" enough to be called a theorem.
There are also results that are important enough to have capitalized names and nevertheless are called lemmas, such as for example Zorn's lemma. This is sometimes a pure accident of history, but also sometimes to suggest that whereas the result does not look particularly interesting on its surface, it is a useful component for proving more substantial propositions.
answered Nov 25 at 3:37
Henning Makholm
238k16303537
answered Nov 25 at 3:37
Henning Makholm
238k16303537
answered Nov 25 at 3:37
Henning Makholm
238k16303537
answered Nov 25 at 3:37
Henning Makholm
238k16303537
238k16303537
Le theoreme de Zorn, Zorn's lemma , a bit of history, perhaps of interest.en.m.wikipedia.org/wiki/Zorn%27s_lemma
– Peter Szilas
Nov 25 at 6:57
add a comment |
Le theoreme de Zorn, Zorn's lemma , a bit of history, perhaps of interest.en.m.wikipedia.org/wiki/Zorn%27s_lemma
– Peter Szilas
Nov 25 at 6:57
Le theoreme de Zorn, Zorn's lemma , a bit of history, perhaps of interest.en.m.wikipedia.org/wiki/Zorn%27s_lemma
– Peter Szilas
Nov 25 at 6:57
Le theoreme de Zorn, Zorn's lemma , a bit of history, perhaps of interest.en.m.wikipedia.org/wiki/Zorn%27s_lemma
– Peter Szilas
Nov 25 at 6:57
add a comment |
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Possible duplicate of Lemma vs. Theorem
– Somos
Nov 25 at 13:39