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In a court of law, a party's claim is a counterclaim if one party asserts claims in response to the claims of another. In other words, if a plaintiff initiates a lawsuit and a defendant responds to the lawsuit with claims of their own against the plaintiff, the defendant's claims are "counterclaims." Examples of counterclaims include:
In logic a counterexample disproves the generalization, and does so rigorously in the fields of mathematics and philosophy. [1] For example, the fact that "student John Smith is not lazy" is a counterexample to the generalization "students are lazy", and both a counterexample to, and disproof of, the universal quantification "all students are ...
A crossclaim is a claim asserted between codefendants or coplaintiffs in a case and that relates to the subject of the original claim or counterclaim according to Black's Law Dictionary. A crossclaim is filed against someone who is a co-defendant or co-plaintiff to the party who originates the crossclaim.
If for example a defendant is in a car accident, and their insurance policy includes an indemnification clause, they can implead their insurance company to pay out the lawsuit. An impleaded party may turn around and sue the original defendant in turn, which is called a crossclaim .
For example, in the case of "compulsory counterclaims," the defendant must assert some form of counterclaim or risk having the counterclaim barred in any subsequent proceeding. In the case of making a counterclaim, the defendant is making a motion directed towards the plaintiff claiming that he/she was injured in some way or would like to sue ...
3. Between two groups, may mean that the first one is a proper subgroup of the second one. > (greater-than sign) 1. Strict inequality between two numbers; means and is read as "greater than". 2. Commonly used for denoting any strict order. 3. Between two groups, may mean that the second one is a proper subgroup of the first one. ≤ 1.
The expression "statistical proof" may be used technically or colloquially in areas of pure mathematics, such as involving cryptography, chaotic series, and probabilistic number theory or analytic number theory. [23] [24] [25] It is less commonly used to refer to a mathematical proof in the branch of mathematics known as mathematical statistics.
In constructive mathematics, "not empty" and "inhabited" are not equivalent: every inhabited set is not empty but the converse is not always guaranteed; that is, in constructive mathematics, a set that is not empty (where by definition, "is empty" means that the statement () is true) might not have an inhabitant (which is an such that ).