Timeline for Can you do math without knowing how to count?
Current License: CC BY-SA 4.0
7 events
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| Apr 20, 2021 at 12:49 | comment | added | user21820 | @Kapil: I would actually argue (related to the point in my answer) that axiomatic euclidean geometry requires you to already believe in natural numbers. If not, there is no guarantee that you can always draw a line between two drawn points and draw a point at intersection of two drawn lines. Because once there are at least 4 points in general position, you can draw infinitely many more if the concept of counting holds up. In other words, if you do not believe all naturals are constructible in some sense, then you cannot believe both of those construction axioms of euclidean geometry. | |
| Apr 18, 2021 at 15:52 | comment | added | Kapil | @AlecRhea One of the "missing" axioms of Euclidean geometry is that there are at least 3 non-collinear points and another states that each line contains at least two points. However, you have encapsulated the axiom I asked about! | |
| Apr 18, 2021 at 12:07 | comment | added | Alex Kruckman | @AlecRhea Nitpick: you need to put the condition $x\neq y$ before the $\exists!$ quantifier. :0) | |
| Apr 18, 2021 at 8:23 | comment | added | PatrickT | Don't you need an algorithm to tell you to stop after two points? Mark point when sun sets, mark point when sun rises, connect morning point with evening point. :-) | |
| Apr 18, 2021 at 4:28 | comment | added | Alec Rhea | @Kapil $\forall x,y\exists!\ell(x\neq y\implies \{x,y\}\subseteq\ell)$? | |
| Apr 18, 2021 at 2:51 | comment | added | Kapil | How do you state "Two distinct points determine a line" without the number two? | |
| Apr 17, 2021 at 17:26 | history | answered | Gerald Edgar | CC BY-SA 4.0 |