Skip to main content
MathOverflow

Return to Answer

http -> https (the question was bumped anyway)
Source Link
Martin Sleziak
Martin Sleziak
  • 4.7k
  • 4
  • 35
  • 40

There's some evidence that precisely the opposite can be said: that Euler is aware of the fallacies of proving theorems by example (of course, this does not necessarily mean he has never used it). One memorable instance is his Exemplum Memorabile Inductionis Fallacis, where he described how he was almost led to conjecture a recursive formula for a particular numerical sequence until he found that they disagreed on the 10th term. (There are other reasons for that formula to have been plausible; that and other topics are discussed in this articlethis article.)

(Incidentally the "right" formula is now quite well-knownnow quite well-known.)

There's some evidence that precisely the opposite can be said: that Euler is aware of the fallacies of proving theorems by example (of course, this does not necessarily mean he has never used it). One memorable instance is his Exemplum Memorabile Inductionis Fallacis, where he described how he was almost led to conjecture a recursive formula for a particular numerical sequence until he found that they disagreed on the 10th term. (There are other reasons for that formula to have been plausible; that and other topics are discussed in this article.)

(Incidentally the "right" formula is now quite well-known.)

There's some evidence that precisely the opposite can be said: that Euler is aware of the fallacies of proving theorems by example (of course, this does not necessarily mean he has never used it). One memorable instance is his Exemplum Memorabile Inductionis Fallacis, where he described how he was almost led to conjecture a recursive formula for a particular numerical sequence until he found that they disagreed on the 10th term. (There are other reasons for that formula to have been plausible; that and other topics are discussed in this article.)

(Incidentally the "right" formula is now quite well-known.)

Source Link
Willie Wong
Willie Wong
  • 39.1k
  • 4
  • 94
  • 176

There's some evidence that precisely the opposite can be said: that Euler is aware of the fallacies of proving theorems by example (of course, this does not necessarily mean he has never used it). One memorable instance is his Exemplum Memorabile Inductionis Fallacis, where he described how he was almost led to conjecture a recursive formula for a particular numerical sequence until he found that they disagreed on the 10th term. (There are other reasons for that formula to have been plausible; that and other topics are discussed in this article.)

(Incidentally the "right" formula is now quite well-known.)

Post Made Community Wiki by Willie Wong