6th Jun '17 2:35:48 PM

**Madrugada** Is there an issue? Send a Message

**Changed line(s) 44,46 (click to see context) from:**

* 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."

** 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."

**to:**

* 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."

**

25th Jan '17 7:31:52 PM

**Game_Fan** Is there an issue? Send a Message

**Changed line(s) 21,22 (click to see context) from:**

* 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!

** 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!

**to:**

* 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.)

** 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

** 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.)

25th Jan '17 7:28:21 PM

**Game_Fan** Is there an issue? Send a Message

**Changed line(s) 21 (click to see context) from:**

* 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.

**to:**

* ~~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!

** An even more dramatic example is [[https://en.wikipedia.

22nd Jun '15 4:15:56 AM

**ShorinBJ** Is there an issue? Send a Message

**Changed line(s) 4 (click to see context) from:**

:: Hasty Generalisation

**to:**

:: Hasty ~~Generalisation~~Generalization

8th Nov '13 6:09:12 PM

**RatherRandomRachel** Is there an issue? Send a Message

**Changed line(s) 45 (click to see context) from:**

** 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."

**to:**

** 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."

23rd Sep '13 3:20:52 AM

**RatherRandomRachel** Is there an issue? Send a Message

**Changed line(s) 45 (click to see context) from:**

** 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.

**to:**

** 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."

23rd Sep '13 3:13:04 AM

**RatherRandomRachel** Is there an issue? Send a Message

**Changed line(s) 45,46 (click to see context) from:**

** 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.

*** That's mathematical induction, which is not "induction" in the logical sense (''i.e.'', inductive reasoning); rather, it is rigorous deductive reasoning.

**to:**

** ~~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.

*** That's mathematical induction, which is not "induction" in the logical sense (''i.e.'', inductive reasoning); rather,

11th Jun '13 2:19:17 PM

**DCC** Is there an issue? Send a Message

**Added DiffLines:**

In short, mistaking inductive reasoning for deductive reasoning

19th May '13 10:19:55 PM

**trumpetmarietta** Is there an issue? Send a Message

**Changed line(s) 43 (click to see context) from:**

** 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...)

**to:**

** 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.

*** That's mathematical induction, which is not "induction" in the logical sense (''i.e.'', inductive reasoning); rather, it is rigorous deductive reasoning.

6th Apr '13 7:22:17 PM

**SenseiLeRoof** Is there an issue? Send a Message

**Changed line(s) 43 (click to see context) from:**

** 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...)

**to:**

** 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...)

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