/sci/ - Science & Math

>>9633044
it's not physical intuition, it's physical knowledge. i can look at the ambient space around me and conclude empirically that no manifold can possibly have such jumps.
consider for example the continuous manifold in the attached drawing. denote it by [math]\mathcal{M}[/math]. then if any jump whatsoever exists in [math]\mathcal{M}[/math], then
[math]\displaystyle \prod_{p ~ \text{prime}} f(x) + \epsilon^p - f'(x) = \infty[/math] for every non-infinitesimal [math]x \in Ext^1_{\underline{\mathbb{Z}}}(\mathcal{M}^{\mathbb{Q}}, \underline{\mathbb{Z}})[/math] assuming f' exists as f' approaches zero which is an obvious contradiction physically speaking.