query: What is the importance of changing the strict inequalities in the definition of a limit to weak inequalities.
positive_passages.docid: 90153
positive_passages.text: Why does the definition of limits of a function have strict inequality?
negative_passages.docid: 85614
negative_passages.text: Do inequalities hold under differentiation?
negative_passages.docid: 103042
negative_passages.text: Is it possible to have Mathematica move all terms to one side of an inequality?
negative_passages.docid: 157215
negative_passages.text: Order of statements in the Delta-Epsilon Limit definition
negative_passages.docid: 84961
negative_passages.text: weak sequential continuity of linear operators
negative_passages.docid: 8842
negative_passages.text: What's wrong with this "backwards" definition of limit?
negative_passages.docid: 128026
negative_passages.text: Weak derivatives equals zero
negative_passages.docid: 148302
negative_passages.text: In convergence, why not $d \leq \epsilon$?
negative_passages.docid: 105107
negative_passages.text: How to explain the following definition of $\lim\sup s_n$ intuitively?
negative_passages.docid: 141318
negative_passages.text: $\subset$ vs $\subseteq$ when *not* referring to strict inclusion
negative_passages.docid: 40458
negative_passages.text: Does scaling lead to weak convergence to the null function?
negative_passages.docid: 142782
negative_passages.text: Operator< and strict weak ordering
negative_passages.docid: 150937
negative_passages.text: Basic Algebra Proof on Integers - Weak Inequalities Work but Strict Inequalities Don't?
negative_passages.docid: 19991
negative_passages.text: Weak convergence, together with convergence of norms, implies strong convergence in a Hilbert space.
negative_passages.docid: 35867
negative_passages.text: Squaring sides of an inequality
negative_passages.docid: 115533
negative_passages.text: Inequality for small values of $t$
negative_passages.docid: 156663
negative_passages.text: Interchanging limit with infimum/supremum