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** Or, for that matter, any philosophy. Or hobby. Or nationality. Pick out the most extreme and most dangerous from any group, you'll likely find horrible people, and they may even say they do horrible things because of their philosophy/hobby/nationality and those who don't do those horrible things too [[NoTrueScotsman aren't true believers/fans/patriots]]. None of this suggests that the philosophy, hobby or nationality is bad in general, let alone bad inherently.


* Fictional UltimateShowdownOfUltimateDestiny comparisons. A popular usage of the "No Limits Fallacy" is to claim that because a specific character's abilities work in a particular setting, it cannot be extrapolated to infinity in another setting. For example, "If [[Webcomic/OnePunchMan Saitama]] can defeat anyone with [[OneHitKO one punch]], then can he defeat Franchise/{{Superman}}, Comicbook/{{Thanos}} with the Infinity Gauntlet, or {{God}} as written in TheBible?". The problem with this question is that fiction does not follow "logical" conclusions; what is stated in the text is true until stated otherwise in the text. We will never know if Saitama could defeat God because the Bible can never be edited to account for Saitama, and even if some [[TheOmnipotent version of God]] were introduced as a character in ''One Punch Man'', it would merely be an {{Expy}} created to serve that specific author's narrative purpose.

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* Fictional UltimateShowdownOfUltimateDestiny comparisons. A popular usage of the "No Limits Fallacy" is to claim that because a specific character's abilities work in a particular setting, it cannot be extrapolated to infinity in another setting. For example, "If [[Webcomic/OnePunchMan Saitama]] can defeat anyone with [[OneHitKO one punch]], then can he defeat Franchise/{{Superman}}, Comicbook/{{Thanos}} with the Infinity Gauntlet, or {{God}} as written in TheBible?".Literature/TheBible?". The problem with this question is that fiction does not follow "logical" conclusions; what is stated in the text is true until stated otherwise in the text. But at the same time, if the text initially assigns something an "infinite" value, adding a limitation later means that the object is no longer "infinite". We will never know if Saitama could defeat God because the Bible can never be edited to account for Saitama, and even if some [[TheOmnipotent version of God]] were introduced as a character in ''One Punch Man'', it would merely be an {{Expy}} created to serve that specific author's narrative purpose.


** A (simple) example of this might be: "A new plant found seems to fit into a particular category with several others. All of the plants within this category seem to need three things to thrive - carbon dioxide, water and a light source. Therefore, it seems likely this plant will also need those three to survive. We should study it to confirm or deny this theory."

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** A (simple) example of this might be: "A new plant found seems to fit into a particular category with several others. All of the plants within this category seem to need three things to thrive - carbon dioxide, water and a light source. Therefore, it seems likely this plant will also need those three to survive. We should study it to confirm or deny this theory.""

* Fictional UltimateShowdownOfUltimateDestiny comparisons. A popular usage of the "No Limits Fallacy" is to claim that because a specific character's abilities work in a particular setting, it cannot be extrapolated to infinity in another setting. For example, "If [[Webcomic/OnePunchMan Saitama]] can defeat anyone with [[OneHitKO one punch]], then can he defeat Franchise/{{Superman}}, Comicbook/{{Thanos}} with the Infinity Gauntlet, or {{God}} as written in TheBible?". The problem with this question is that fiction does not follow "logical" conclusions; what is stated in the text is true until stated otherwise in the text. We will never know if Saitama could defeat God because the Bible can never be edited to account for Saitama, and even if some [[TheOmnipotent version of God]] were introduced as a character in ''One Punch Man'', it would merely be an {{Expy}} created to serve that specific author's narrative purpose.


* Proving an existential statement (i.e. "There exists...") by example. One example is plenty.
** The prime (pardon the pun) example might well be this: "2 is an even number and is prime. Therefore, there exists at least one prime number that is even."

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* Proving an existential statement (i.e. "There exists...") by example. One example is plenty.
**
all that's needed. The prime (pardon the pun) example might well be this: "2 is an even number and is prime. Therefore, there exists at least one prime number that is even."


* In mathematics proof by example is no proof at all. One instance of this is a conjecture by Christian Goldbach that "every odd composite number can be written as the sum of a prime and twice a square number" which certainly seems to be true if you try casually testing a few example. It wasn't until much later that a counter example (5777) was found.
** An even more dramatic example is [[https://en.wikipedia.org/wiki/Euler%27s_sum_of_powers_conjecture Euler's sum of power conjecture]] for which the first counter example is 61,917,364,224!

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* In mathematics proof by example is usually no proof at all. One instance of this Many famous examples are used to illustrate this.
** A simple one
is a conjecture by Christian Goldbach that "every odd composite number can be written as the sum of a prime and twice a square number" which certainly seems to be true if you try casually testing a few example. It wasn't until much later that a counter example (5777) was found.
** An even more dramatic example is [[https://en.wikipedia.org/wiki/Euler%27s_sum_of_powers_conjecture Euler's sum of power conjecture]] for which the first counter example counter-example is 61,917,364,224!61,917,364,224!
** There are problem in mathematics that have been tested for trillions upon trillions of examples without finding a counter-example but still lack proof. (The huge numbers of examples are both used to search for counter-examples and in hopes of discovering patterns that might lead to a proof.)


* Usually, in mathematics, [[http://en.wikipedia.org/wiki/Skewe%27s_number no matter how many examples]] [[http://en.wikipedia.org/wiki/Riemann_hypothesis you might have]], proof by example is not a good idea.

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* Usually, in mathematics, [[http://en.In mathematics proof by example is no proof at all. One instance of this is a conjecture by Christian Goldbach that "every odd composite number can be written as the sum of a prime and twice a square number" which certainly seems to be true if you try casually testing a few example. It wasn't until much later that a counter example (5777) was found.
** An even more dramatic example is [[https://en.
wikipedia.org/wiki/Skewe%27s_number no matter how many examples]] [[http://en.wikipedia.org/wiki/Riemann_hypothesis you might have]], proof by org/wiki/Euler%27s_sum_of_powers_conjecture Euler's sum of power conjecture]] for which the first counter example is not a good idea.61,917,364,224!


:: Hasty Generalisation

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:: Hasty GeneralisationGeneralization


** A (simple) example of this might be: "A new plant found seems to fit into a particular category with several others. All of the plants within this category need three things to thrive - carbon dioxide, water and a light source. Therefore, it seems likely this plant will also need those three to survive. We should study it to confirm or deny this theory."

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** A (simple) example of this might be: "A new plant found seems to fit into a particular category with several others. All of the plants within this category seem to need three things to thrive - carbon dioxide, water and a light source. Therefore, it seems likely this plant will also need those three to survive. We should study it to confirm or deny this theory."


** A (simple) example of this might be: A new plant found seems to fit into a particular category with several others. All of the plants within this category need three things to thrive - carbon dioxide, water and a light source. Therefore, it seems likely this plant will also need those three to survive. We should study it to confirm or deny this theory.

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** A (simple) example of this might be: A "A new plant found seems to fit into a particular category with several others. All of the plants within this category need three things to thrive - carbon dioxide, water and a light source. Therefore, it seems likely this plant will also need those three to survive. We should study it to confirm or deny this theory."


** To clarify. Induction - at its most basic is proving it by proving two things. The Base Case exists (typically for the value of 1 or 0) and that if we assume the theory works at value k (k being any given number) we can prove that it works at k+1. Combine the two and you get the ladder (1 is true, which means 1+1 is true, which means 2+1 is true...)
*** That's mathematical induction, which is not "induction" in the logical sense (''i.e.'', inductive reasoning); rather, it is rigorous deductive reasoning.

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** To clarify. Induction - at its most basic is proving it by proving two things. The Base Case exists (typically for A (simple) example of this might be: A new plant found seems to fit into a particular category with several others. All of the value of 1 or 0) plants within this category need three things to thrive - carbon dioxide, water and that if we assume the theory works at value k (k being any given number) we can prove that a light source. Therefore, it works at k+1. Combine the two and you get the ladder (1 is true, which means 1+1 is true, which means 2+1 is true...)
*** That's mathematical induction, which is not "induction" in the logical sense (''i.e.'', inductive reasoning); rather,
seems likely this plant will also need those three to survive. We should study it is rigorous deductive reasoning.to confirm or deny this theory.

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In short, mistaking inductive reasoning for deductive reasoning


** To clarify. Induction - at its most basic is proving it by proving two things. The Base Case exists (typically for the value of 1 or 0) and that if we assume the theory works at value k (k being any given number) we can prove that it works at k+1. Combine the two and you get the ladder (1 is true, which means 1+1 is true, which means 2+1 is true...)

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** To clarify. Induction - at its most basic is proving it by proving two things. The Base Case exists (typically for the value of 1 or 0) and that if we assume the theory works at value k (k being any given number) we can prove that it works at k+1. Combine the two and you get the ladder (1 is true, which means 1+1 is true, which means 2+1 is true...))
*** That's mathematical induction, which is not "induction" in the logical sense (''i.e.'', inductive reasoning); rather, it is rigorous deductive reasoning.


** To clarify. Induction - at it's most basic is proving it by proving two things. THe Base Case exists (typically for the value of 1 or 0) and that if we assume the theory works at value k (k being any given number) we can prove that it works at k+1. Combine the two and you get the ladder (1 is true, which means 1+1 is true, which means 2+1 is true...)

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** To clarify. Induction - at it's its most basic is proving it by proving two things. THe The Base Case exists (typically for the value of 1 or 0) and that if we assume the theory works at value k (k being any given number) we can prove that it works at k+1. Combine the two and you get the ladder (1 is true, which means 1+1 is true, which means 2+1 is true...)


* An attempt at real induction. Inductive logic admits that its conclusions are not ''necessarily'' true, but rather that they are ''probably'' true, and it tends to attempt to be as exhaustive as possible and to eliminate as many alternative explanations as possible, to reduce the possibility that the conclusion is wrong to as close to zero as possible. However, an honest scientist (i.e. practitioner of inductive logic) would freely admit that there is the possibility, however slim, that the entirety of his/her science is entirely wrong.

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* An attempt at real induction. Inductive logic admits that its conclusions are not ''necessarily'' true, but rather that they are ''probably'' true, and it tends to attempt to be as exhaustive as possible and to eliminate as many alternative explanations as possible, to reduce the possibility that the conclusion is wrong to as close to zero as possible. However, an honest scientist (i.e. practitioner of inductive logic) would freely admit that there is the possibility, however slim, that the entirety of his/her science is entirely wrong.wrong.
** To clarify. Induction - at it's most basic is proving it by proving two things. THe Base Case exists (typically for the value of 1 or 0) and that if we assume the theory works at value k (k being any given number) we can prove that it works at k+1. Combine the two and you get the ladder (1 is true, which means 1+1 is true, which means 2+1 is true...)


* When you are ''disproving'' by example.

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* When you are ''disproving'' by example.
example -- this is termed a "counter-example."

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