In logic, rhetoric and mathematics, a counterexample is an example, a particular case or a general result, which contradicts first impressions. A counterexample can also be given to reject a conjecture, i.e. a statement that people (and in particular mathematicians) thought to be true.
Example: All our lives we see white swans. We therefore make the inference that all swans are white, until an event changes our perception of reality. For example, if we see a black swan, we question our representation of reality.
How do you find a counterexample in math?
Unlike in everyday life, where it is customary to say that the exception confirms the rule, in mathematics the existence of an exception invalidates the rule.
This method is used very early in mathematical practice either to disprove a conjecture or to prove that a property is not realised. Thus, to prove that a real function f is not even, it is sufficient to show a single real x for which f(x) differs from f(-x) whereas, to prove that the function is even, it would be necessary to show that the equality f(x) = f(-x) is true for any real x belonging to the set of definition of f.
What is a characterization in math?
In mathematical language, the characterisation of an object X by a property P means that not only does X possess property P, but also that X is the only object that possesses property P. It is also quite common to come across statements such as “property Q characterises Y to within an isomorphism”, which indicates that the objects verifying Q are exactly the objects that are isomorphic to Y. (Instead of “isomorphism” in the expression “to within an isomorphism of Y”, some other “relation of equivalence between objects” could be specified)
Are there any inconsistencies in math?
For math to be consistent, there can’t be contradictions. Mathematics is very precise. So first define these things you talk about and then you can consider contradictions (which you won’t find). There’s a big difference between a contradiction and a paradox (the latter only seems impossible).
What is the meaning of the word counterexample in this particular topic?
A counterexample is a special kind of example that disproves a statement or proposition. Counterexamples are often used in math to prove the boundaries of possible theorems.
What is a counterexample example?
An example that disproves a statement (shows that it is false). Example: the statement “all dogs are hairy” can be proved false by finding just one hairless dog (the counterexample) like below.
What is a counter example give example?
A counterexample to the statement “all prime numbers are odd numbers” is the number 2, as it is a prime number but is not an odd number. Neither of the numbers 7 or 10 is a counterexample, as neither of them are enough to contradict the statement.
Is counter example one word?
“Counterexample.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/counterexample. Accessed 20 Jun.
What is a counter example geometry?
A counterexample is an example in which the hypothesis is true, but the conclusion is false. If you can find a counterexample to a conditional statement, then that conditional statement is false.
What is counterexample explain how counter example helps in problem solving?
Counterexample is an example with a negative connotation. Whereas an example may be used to support or illustrate a claim, a counterexample is used to refute an assertion. How an example is being used often depends on the purpose or the formulation.
What is another word for counter example?
n. disproof, falsification, refutation.
What is another word for counter effect?
neutralize, counterbalance, contravene, thwart.
What’s a synonym for counterintuitive?
Words related to counterintuitive
unreasonable, faulty, illogical, implausible, nonsensical, absurd, capricious, contradictory, erratic, preposterous, reasonless, senseless, sophistic, untenable.
What is another word for refutation?
In this page you can discover 29 synonyms, antonyms, idiomatic expressions, and related words for refutation, like: refuting, rebuttal, denial, disprove, invalidate, repeal, falsification, falsifying, refutal, defense and defence.
What is an example of refutation?
Examples of Refutation: A defense attorney would refute the prosecutor’s statement that his client is guilty by providing evidence or logical statements that refute the claim. For example, in the O.J. Simpson murder trial, the prosecutor tried to argue that the bloody gloves found were Simpson’s.
What is another word for counter argument?
Counter-argument Synonyms – WordHippo Thesaurus.
What is another word for counter-argument?