>>38
"every real number is larger than a rational therefore there are no infinitesimals in the reals."
That doesn't make sense. 1 is a real number, and it is not greater than the rational number 2. Even if it were true, it says nothing about infinitesimals.
For every real number, I can pick a smaller rational number.
For every rational number, I can pick a smaller real number.
The rest of what you said is true.