Timeline for Theorems that are 'obvious' but hard to prove
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Jan 10, 2011 at 22:32 | history | edited | Jason | CC BY-SA 2.5 |
elaborated on my point
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| Jan 10, 2011 at 5:03 | comment | added | Jason | My point was that given you know a statement is in the theory of the Natural numbers, if you were asked whether it were true or not, you'd be able to respond without hesitation with an affirmative answer. | |
| Jan 10, 2011 at 4:29 | comment | added | Jason | By definition, the theory of the Natural numbers is the collection of all statements in the language of arithmetic that are true in $\mathbb{N}$. When we say that a statement in the language of arithmetic is true, we mean that is true in $\mathbb{N}$. Consequently, a statement in the language of arithmetic is true if and only if it is in the theory of the Natural numbers. The argument of whether the statement is in the theory of the Natural numbers takes place in the set-theoretic universe $V$, which models all of the theorems of ZFC. | |
| Jan 10, 2011 at 4:00 | comment | added | Chris Eagle | What is this definition of "obviously true" that makes these obviously true? | |
| Jan 10, 2011 at 3:50 | history | answered | Jason | CC BY-SA 2.5 |