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When was Counterexamples in Topology created?

Counterexamples in Topology was created in 1978.


How many pages does Counterexamples in Topology have?

Counterexamples in Topology has 244 pages.


How do you solve a remainder theorem?

You cannot solve a theorem: you can prove the theorem or you can solve a question based on the remainder theorem.


Does science offer conclusive proof for a theory?

Sometimes Yes, as in Pythagoras' Theorem. Other times No, for as Godel's Incompleteness Theorem shows, there will be complete bodies of knowledge in which there will be truths that cannot be proven, and falsities which cannot be denied. [I paraphrase his theorem.]


Are there any similarities between a theorem and an axiom?

A theorem is a proved rule but an axiom cannot be proven but is stated to be true.


How do you work out pythagorean theorem with only one side?

You cannot.


Can a theorem have a counterexample?

No, a theorem cannot have a counterexample, as a theorem is a statement that has been proven to be true under a specific set of conditions. A counterexample, on the other hand, demonstrates that a statement or conjecture is false by providing an instance where the statement does not hold. If a counterexample exists, the statement is not a theorem.


Is every quadrilateral a parellelogram?

No. There are many counterexamples including trapezoids and kites.


How many counterexamples are required to prove that a conjecture is false?

One is enough.


Is PQR XYZ If so name which similarity postulate or theorem applies?

cannot be determined


How do you use the ideas of counterexamples to verify valid conjectures and refute invalid conjectures?

Counterexamples are used to test the validity of conjectures by providing a specific instance where a conjecture fails. If a counterexample is found, it refutes the conjecture, demonstrating that it is invalid. Conversely, if no counterexamples can be found despite thorough testing, it supports the conjecture's validity, although this does not prove it universally true. Thus, while counterexamples are critical for refutation, their absence strengthens the case for a conjecture, though further proof may still be needed for confirmation.


Why Lami's theorem cannot be used for 4 concurrent forces?

Because, this theorem comes from the law of sines which is completely a triangle law and the law of sines can not be applied on other polygons.