Smooth Infinitesimal Analysis posits an infinitesimal such that the following statements are both true:

This is a very promising idea, but the way they pose it leans on ignoring the law of excluded middle, which is a little unsettling. I propose a different interpretation of the same definitions. In geometric algebra, squaring erases direction, as seen in how the basis vectors square:

In light…

Even entry-level oscilloscopes today have simple math functions such as adding or subtracting two channels. But as Arthur Pini] notes, more advanced scopes can now even do integration and differentiation. […read more