Mixing
The price of constructivity
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It is said that proofs in constructive math, if possible at all, tend to be more verbose than in classical math. I'm trying to get an intuition for this, so:
Are there any good example of theorems mathematicians use, for which the proof in constructive math is considerably larger that the proof in classical math?
I'm not looking for artificial examples like in this question (https://mathoverflow.net/questions/294092/g%c3%b6dels-speed-up-from-constructive-to-classical-logic), but rather for meaningful theorems.
constructive-mathematics
asked Jan 23 at 10:28
ternaryternary
61
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add a comment |
$begingroup$
It is said that proofs in constructive math, if possible at all, tend to be more verbose than in classical math. I'm trying to get an intuition for this, so:
Are there any good example of theorems mathematicians use, for which the proof in constructive math is considerably larger that the proof in classical math?
I'm not looking for artificial examples like in this question (https://mathoverflow.net/questions/294092/g%c3%b6dels-speed-up-from-constructive-to-classical-logic), but rather for meaningful theorems.
constructive-mathematics
asked Jan 23 at 10:28
ternaryternary
61
$endgroup$
$begingroup$
It's not a surprise constructive proofs are longer than classical proofs: every constructive proof is a classical proof and it usually proves more.
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– lhf
Jan 23 at 10:32
1
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@lhf: It's not a surprise indeed. But I'm wondering if there are particular cases where this fact has most impact.
$endgroup$
– ternary
Jan 23 at 10:34
add a comment |
$begingroup$
It is said that proofs in constructive math, if possible at all, tend to be more verbose than in classical math. I'm trying to get an intuition for this, so:
Are there any good example of theorems mathematicians use, for which the proof in constructive math is considerably larger that the proof in classical math?
I'm not looking for artificial examples like in this question (https://mathoverflow.net/questions/294092/g%c3%b6dels-speed-up-from-constructive-to-classical-logic), but rather for meaningful theorems.
constructive-mathematics
asked Jan 23 at 10:28
ternaryternary
61
$endgroup$
It is said that proofs in constructive math, if possible at all, tend to be more verbose than in classical math. I'm trying to get an intuition for this, so:
Are there any good example of theorems mathematicians use, for which the proof in constructive math is considerably larger that the proof in classical math?
I'm not looking for artificial examples like in this question (https://mathoverflow.net/questions/294092/g%c3%b6dels-speed-up-from-constructive-to-classical-logic), but rather for meaningful theorems.
constructive-mathematics
constructive-mathematics
asked Jan 23 at 10:28
ternaryternary
61
asked Jan 23 at 10:28
ternaryternary
61
asked Jan 23 at 10:28
ternaryternary
61
asked Jan 23 at 10:28
ternaryternary
61
asked Jan 23 at 10:28
ternaryternary
61
61
$begingroup$
It's not a surprise constructive proofs are longer than classical proofs: every constructive proof is a classical proof and it usually proves more.
$endgroup$
– lhf
Jan 23 at 10:32
1
$begingroup$
@lhf: It's not a surprise indeed. But I'm wondering if there are particular cases where this fact has most impact.
$endgroup$
– ternary
Jan 23 at 10:34
add a comment |
$begingroup$
It's not a surprise constructive proofs are longer than classical proofs: every constructive proof is a classical proof and it usually proves more.
$endgroup$
– lhf
Jan 23 at 10:32
1
$begingroup$
@lhf: It's not a surprise indeed. But I'm wondering if there are particular cases where this fact has most impact.
$endgroup$
– ternary
Jan 23 at 10:34
$begingroup$
It's not a surprise constructive proofs are longer than classical proofs: every constructive proof is a classical proof and it usually proves more.
$endgroup$
– lhf
Jan 23 at 10:32
$begingroup$
It's not a surprise constructive proofs are longer than classical proofs: every constructive proof is a classical proof and it usually proves more.
$endgroup$
– lhf
Jan 23 at 10:32
1
1
$begingroup$
@lhf: It's not a surprise indeed. But I'm wondering if there are particular cases where this fact has most impact.
$endgroup$
– ternary
Jan 23 at 10:34
$begingroup$
@lhf: It's not a surprise indeed. But I'm wondering if there are particular cases where this fact has most impact.
$endgroup$
– ternary
Jan 23 at 10:34
add a comment |
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$begingroup$
It's not a surprise constructive proofs are longer than classical proofs: every constructive proof is a classical proof and it usually proves more.
$endgroup$
– lhf
Jan 23 at 10:32
1
$begingroup$
@lhf: It's not a surprise indeed. But I'm wondering if there are particular cases where this fact has most impact.
$endgroup$
– ternary
Jan 23 at 10:34