202408191743 Geometry 0

$\forall$ : for all/any/each/every
$\exists$ : there exist(s)/is/are

If, in any event $(x,y,z,t)$ :

i. no two points $a$ and $b$ occupy the same position. I.e.,

$\forall\, t\, \nexists\, a(\neq b)\enspace\textrm{s.t. }(x_a,y_a,z_a)=(x_b,y_b,z_b)$

ii. none any point $a$ occupies more than one position. I.e.,

$\forall\,a,t\,\exists\, !\mathbf{r}\enspace\textrm{s.t. }a\stackrel{\mathbf{r}(t)}{\longmapsto}(x_a,y_a,z_a)$

such points are said to be mass particles; or else massless particles.

(to be continued)