Abraham Robinson's non-standard analysis also used infinitesimal distinctions to produce a calculus. But both these instances where empirically defined distinctions, such as the scissors's junction, or the point of overlap or contrast. The true infinitesimal is not an imaginary number, and this is my theory (I have only found a contemporary mathematician who agrees, named Pena, the editor of Sorites in Spain), the real infinitesimal is one, and there can be only one, and every instance of number "one," as any reference to one-self (and Schrodinger would agree) is the numerically one, the real beginning of the number line (and continuum, not at dimension one, but at the First Distinction, dimension one is the first extension), as I suggest that zero is only a number as much as the Absolute Infinite is. The so-called origin is not zero, but one, and the ultimate reality of the real numbers is what they are only in reference to as a whole (taken in the first place to be one, all numbers) and they are N over (fractional) Infinity, and One is Unity Over Infinity, the real Infinitesimal, There Can Be Only One (to quote M. Lambert).
See what I did? Zero doesn't exist. Nothing is just that. Non-being does not exist. That part is so very simple. But wait, it's all quite simple...
Oneness is being-in-itself, which is pure self-reference. One is absolutely imaginary in its staticity, since its reference to the Other (transcendentally, the Infinitely and Totally Other which Levinas speaks of, to label the Infinite as teh Other or pure Objectivity or Superjectivity) manifests in-so-much as Other Numbers manifest. In other words, One refers to whatever number has already been counted this time (empirically), otherwise it only refers to the Infinite.
Infinity is overwhelming. To capture its meaning is futile. We do have a word for it, but etymologically it is a negative word meaning "not-finite" where "finite" refers to our state of being, which is not the state of being-in-itself (the first phase of phase-locked space) but of beings (to make the ontico-ontological distinction) wherein we are taken to be only one of them (so-called finite). But we are one, the Subejct of the sentence, and of the universe of discourse, we are singular, I am. I am pure subjectivity in the absolute sense, and you are too, and so are we. So 'we' means one too.
Infinity is in permanent super-position, for it to be posited requires not perfect superjectivity (objectivity) but perfect subjectivity, which is the Spirit which animates us. The Absolute Value of the Infinite (the Infinities of pluralists, including trans-finities) is the Absolute Infinite. The Absolute Infinite is Ultimate Reality. That's a bold declarative statement.
The Absolute Infinite is Ultimate Reality.
The Infinitesimal is Pen-Ultimate Reality.
There can be only one Infinitesimal, and it is Unity over Infinity, the Unity of Infinity, Spinoza and Plotinus' Infinity, as if 'The One'.
Now is the time for these secrets to be revealed, and this is the place of it.
The Zero doesn't exist, and if you demand it to be, you must acknowledge your one-ness, and your two-valued logic. But ultimately you are One, and you are the origin of reality.
Thanks a lot,