A false statement that can't be disproved without using a counterexample
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When one wants to disprove a statement, finding a counterexample is easier than 'proving a statement is false' in most cases(I don't know if I'm using the right expression here, but I hope you know what I mean). So I thought that some statements might have obvious counterexamples already known, but can't be proven false without counterexamples(or nobody has found the way to do so).
Are there really such a statement?
logic examples-counterexamples proof-theory
asked Nov 17 at 13:47
NumberTWO
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up vote
-1
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When one wants to disprove a statement, finding a counterexample is easier than 'proving a statement is false' in most cases(I don't know if I'm using the right expression here, but I hope you know what I mean). So I thought that some statements might have obvious counterexamples already known, but can't be proven false without counterexamples(or nobody has found the way to do so).
Are there really such a statement?
logic examples-counterexamples proof-theory
asked Nov 17 at 13:47
NumberTWO
1
A counter-example is used to prove the falsity of a "general" statement. But we have also "particular" ones, like e.g. the statement asserting taht the square root if $2$ is rational : in this case, we have to use a proof by contradiction.
– Mauro ALLEGRANZA
Nov 17 at 14:05
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
When one wants to disprove a statement, finding a counterexample is easier than 'proving a statement is false' in most cases(I don't know if I'm using the right expression here, but I hope you know what I mean). So I thought that some statements might have obvious counterexamples already known, but can't be proven false without counterexamples(or nobody has found the way to do so).
Are there really such a statement?
logic examples-counterexamples proof-theory
asked Nov 17 at 13:47
NumberTWO
1
When one wants to disprove a statement, finding a counterexample is easier than 'proving a statement is false' in most cases(I don't know if I'm using the right expression here, but I hope you know what I mean). So I thought that some statements might have obvious counterexamples already known, but can't be proven false without counterexamples(or nobody has found the way to do so).
Are there really such a statement?
logic examples-counterexamples proof-theory
logic examples-counterexamples proof-theory
asked Nov 17 at 13:47
NumberTWO
1
asked Nov 17 at 13:47
NumberTWO
1
asked Nov 17 at 13:47
NumberTWO
1
asked Nov 17 at 13:47
NumberTWO
1
asked Nov 17 at 13:47
NumberTWO
1
1
A counter-example is used to prove the falsity of a "general" statement. But we have also "particular" ones, like e.g. the statement asserting taht the square root if $2$ is rational : in this case, we have to use a proof by contradiction.
– Mauro ALLEGRANZA
Nov 17 at 14:05
add a comment |
A counter-example is used to prove the falsity of a "general" statement. But we have also "particular" ones, like e.g. the statement asserting taht the square root if $2$ is rational : in this case, we have to use a proof by contradiction.
– Mauro ALLEGRANZA
Nov 17 at 14:05
A counter-example is used to prove the falsity of a "general" statement. But we have also "particular" ones, like e.g. the statement asserting taht the square root if $2$ is rational : in this case, we have to use a proof by contradiction.
– Mauro ALLEGRANZA
Nov 17 at 14:05
A counter-example is used to prove the falsity of a "general" statement. But we have also "particular" ones, like e.g. the statement asserting taht the square root if $2$ is rational : in this case, we have to use a proof by contradiction.
– Mauro ALLEGRANZA
Nov 17 at 14:05
add a comment |
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A counter-example is used to prove the falsity of a "general" statement. But we have also "particular" ones, like e.g. the statement asserting taht the square root if $2$ is rational : in this case, we have to use a proof by contradiction.
– Mauro ALLEGRANZA
Nov 17 at 14:05