query: Define infinitesimally small?
positive_passages.docid: 21367
positive_passages.text: Is the theory of dual numbers strong enough to develop real analysis, and does it resemble Newton's historical method for doing calculus?
negative_passages.docid: 105678
negative_passages.text: Smaller vs. less vs. lesser
negative_passages.docid: 153935
negative_passages.text: A weaker Axiom of Infinity?
negative_passages.docid: 5105
negative_passages.text: Alternative definition of $\|f\|_{\infty}$ as the smallest of all numbers of the form $\sup\{|g(x)| : x \in X \}$, where $f = g$ almost everywhere
negative_passages.docid: 132298
negative_passages.text: How do you find the smallest of homeomorphic ordinals?
negative_passages.docid: 94433
negative_passages.text: Rigorous underpinnings of infinitesimals in physics
negative_passages.docid: 147413
negative_passages.text: Meaning of the phrase "little too"?
negative_passages.docid: 10579
negative_passages.text: Can something become "increasingly smaller"?
negative_passages.docid: 63313
negative_passages.text: Uniqueness of Powerseries in an arbitrarily small neighborhood of $0$ in $\mathbb C$
negative_passages.docid: 101372
negative_passages.text: Questions concerning smallest fraction between two given fractions.
negative_passages.docid: 74498
negative_passages.text: Smallest dense subset of $\mathbb{R}$
negative_passages.docid: 65473
negative_passages.text: How can something finite become infinite?
negative_passages.docid: 5371
negative_passages.text: If a function has a finite limit at infinity, does that imply its derivative goes to zero?
negative_passages.docid: 146837
negative_passages.text: Why “characteristic zero” and not “infinite characteristic”?
negative_passages.docid: 9969
negative_passages.text: Is infinity a real number?
negative_passages.docid: 106881
negative_passages.text: Does "finite" include zero?
negative_passages.docid: 5022
negative_passages.text: Can a set containing $0$ be purely imaginary?