Statements such as the Banach – Tarski paradox can be rephrased as conditional statements, for example, " If AC holds, the decomposition in the Banach – Tarski paradox exists.

For example, naive Bayes and linear discriminant analysis are joint probability models, whereas logistic regression is a conditional probability model.

Many of the techniques mentioned here will require extensions to the Web Ontology Language ( OWL ) for example to annotate conditional probabilities.

See, for example, the case of Meyer v. Mitnick, 625 N. W. 2d 136 ( Michigan, 2001 ), whose ruling found the following reasoning persuasive: " the so-called ' modern trend ' holds that because an engagement ring is an inherently conditional gift, once the engagement has been broken, the ring should be returned to the donor.

As example, a conditional branch when the top-of-stack value is zero might be encoded as follows.

This is to be contrasted with an indicative conditional, which indicates what is ( in fact ) the case if its antecedent is ( in fact ) true — for example, " if you drink this, it will make you well ".

This example is closely related to the concept of conditional probability.

For example, macros replaced with aggressive inlining and templates, includes with compile-time imports ( this requires the preservation of type information in the object code, making this feature impossible to retrofit into a language ); conditional compilation is effectively accomplished with and dead code elimination in some languages.

In some cases, re-buys are conditional ( for example, offered only to players low on or out of chips ) but in others they are available to all players ( called add-ons ).

Curry's paradox uses a particular kind of self-referential conditional sentence, as demonstrated in this example:

For example, substituting propositions in natural language for logical variables, the inverse of the conditional proposition, " If it's raining, then Sam will meet Jack at the movies " is " If it's not raining, then Sam will not meet Jack at the movies.

The Zelaya administration had growing friction with the United States government, for example while the French government had inquired to the U. S. whether a loan to Nicaragua would be deemed unfriendly, the U. S. secretary of state required the loan to be conditional on U. S. relations.

If more than one statement is to be controlled by the conditional in the example above, we can use BEGIN and END like this:

For example, during the credit crisis of 2008, the US Federal Reserve indicated rates would be low for an “ extended period ”, and the Bank of Canada made a “ conditional commitment ” to keep rates at the lower bound of 25 basis points ( 0. 25 %) until the end of the second quarter of 2010.

It is possible to combine them with @ Functions, for example by making execution of an @ command conditional on a field value.

One example is that, in contrast with Polish, Silesian retains the pluperfect ( — " I had slipped ") and separate past conditional ( — " I would have slipped ").

Another example of a case requiring conditional baptism would be where an emergency baptism has been performed, if impure water was used the validity of the baptism may be in question.

The branch predictor may, for example, recognize that the conditional jump is taken more often than not, or that it is taken every second time.

For example, a loop-closing conditional jump is mispredicted once rather than twice.

Assume, for example, that a conditional jump is taken every third time.

For example, if the response has a Last-Modified header, a cache can make a conditional request using the If-Modified-Since header to see if it has changed.

For example, given a Bayes network with a set of conditionally independent identically distributed Gaussian-distributed nodes with conjugate prior distributions placed on the mean and variance, the conditional distribution of one node given the others after compounding out both the mean and variance will be a Student's t-distribution.

For example, in the case of variables whose conditional distribution is not easy to sample from, a single iteration of slice sampling or the Metropolis-Hastings algorithm can be used to sample from the variables in question.

A loop may, for example, consist of a connector where control first enters, processing steps, a conditional with one arrow exiting the loop, and one going back to the connector.

For example, the proof that the column rank of a matrix over a field equals its row rank yields for matrices over division rings only that the left column rank equals its right row rank: it does not make sense to speak about the rank of a matrix over a division ring.

" Hello world " is also used by computer hackers as a proof of concept that arbitrary code can be executed through an exploit where the system designers did not intend code to be executed — for example, on Sony's PlayStation Portable.

A writ of habeas corpus, also known as the Great Writ, is a summons with the force of a court order ; it is addressed to the custodian ( a prison official for example ) and demands that a prisoner be taken before the court, and that the custodian present proof of authority, allowing the court to determine whether the custodian has lawful authority to detain the person.

' In the second case, he cites an example that demonstrates ignorance of statistical principles in the lay press: ' Since no such proof is possible genetically modified food is harmless, the article in The New York Times was what is called a " bad rap " against the U. S. Department of Agriculture-a bad rap based on a junk-science belief that it's possible to prove a null hypothesis.

For example, the old instructions on burden of proof in civil cases read:

The above proof is an example of a non-constructive proof disallowed by intuitionists:

In 370 BC, Plato's Parmenides may have contained an early example of an implicit inductive proof.

An example of a theorem from geometric model theory is Hrushovski's proof of the Mordell – Lang conjecture for function fields.

The first example of this is a mathematical proof of the confinement mechanisms in EROS, based on a simplified model of the EROS API.

This method is used, for example, in the proof that there is no free complete lattice.

For example, Russell's paradox suggests a proof that the class of all sets which do not contain themselves is proper, and the Burali-Forti paradox suggests that the class of all ordinal numbers is proper.

( For example, the Coq proof assistant system features a tactic for Presburger arithmetic.

For example, in an axiomatic system, proof of soundness amounts to verifying the validity of the axioms and that the rules of inference preserve validity ( or the weaker property, truth ).

These subjective judgments vary not only from person to person, but also with time: for example, as a proof is simplified or better understood, a theorem that was once difficult may become trivial.

Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group.

If proof emerges of the true extent of the state actor's involvement, this strategy can backfire ; for example see Iran-contra and Philip Agee.

For example, the credit card network does not require a personal identification number for authentication of the claimed identity ; and a small transaction usually does not even require a signature of the authenticated person for proof of authorization of the transaction.

For example, Euclid provides an elaborate proof of the Pythagorean theorem, by using addition of areas instead of the much simpler proof from similar triangles, which relies on ratios of line segments.

For example a person's survival of a near-death illness may be taken as evidence of their power as a healer: in Bali a medium's survival is proof of her association with a patron deity and therefore her ability to communicate with other gods and spirits.

For example, by 1952 members of the SS like Otto Skorzeny could be declared formally denazified () in absentia by a German government arbitration board and without any proof that this was true.

Pliny's career is commonly considered as a summary of the main Roman public charges and is the best-documented example from this period, offering proof for many aspects of imperial culture.

This property enables-adic numbers to encode congruence information in a way that turns out to have powerful applications in number theory including, for example, in the famous proof of Fermat's Last Theorem by Andrew Wiles.