Ask
Type a question and get back our own material — worked solutions, chapters, counterexamples — with a link to each one.
Things it can already settle
Every one of these is a claim that sounds true and is not, with the object that kills it written out. Open one, or type your own question above.
Is it true that Closed and bounded ⇒ compact?
Metric SpacesIs it true that Bounded ⇒ totally bounded?
Metric SpacesIs it true that Completeness is a topological property?
Metric SpacesIs it true that Connected ⇒ path-connected?
Metric SpacesIs it true that Continuous on a bounded interval ⇒ bounded?
Continuity and DifferentiationIs it true that aₙ → 0 ⇒ Σaₙ converges?
The Real LineIs it true that Same characteristic polynomial ⇒ similar?
Eigenvalues and Canonical FormsIs it true that Real matrix with real eigenvalues is diagonalisable?
Eigenvalues and Canonical FormsIs it true that Converse of Lagrange: d | |G| ⇒ subgroup of order d?
GroupsIs it true that Every integral domain is a UFD?
Rings and FieldsIs it true that |f| bounded near an isolated singularity ⇒ pole?
Singularities and ResiduesIs it true that Every IVP has a unique solution?
Ordinary Differential Equations
That is a sample of the counterexample bank; it also searches the chapters and every solved previous-year question.
Verification
Why this doesn’t make things up
It never does the mathematics
It finds a passage someone wrote and checked, and hands it over. It does not compute, rewrite or paraphrase — so there is nothing for it to get wrong.
Everything is checked first
722 solved questions, each verified against the official answer key and, where the mathematics allows, against a symbolic algebra system.
It admits what it doesn’t know
Where nothing matches, it says so rather than guessing. Those questions become the list of what gets written next.
Looking for a specific page instead? PressCtrl+Kanywhere for search, or start from the syllabus.