Such a definition can be formulated in terms of equivalence classes of smooth functions on M. Informally, we will say that two smooth functions f and g are equivalent at a point x if they have the same first-order behavior near x.

Informally known as " The Big Book " ( with its first 164 pages virtually unchanged since the 1939 edition ), it suggests a twelve-step program in which members admit that they are powerless over alcohol and need help from a " higher power "; seek guidance and strength through prayer and meditation from God or Higher Power of their own understanding ; take a moral inventory with care to include resentments ; list and become ready to remove character defects ; list and make amends to those harmed, and then try to help other alcoholics recover.

Informally, this is true because polynomial time algorithms are closed under composition.

Informally basis vectors are like " building blocks of a vector ", they are added together to make a vector, and the coordinates are the number of basis vectors in each direction.

Informally we can think of elements of the Lie algebra as elements of the group that are " infinitesimally close " to the identity, and the Lie bracket is something to do with the commutator of two such infinitesimal elements.

Informally, a soundness theorem for a deductive system expresses that all provable sentences are true.

Informally, the term measure word is also sometimes used to refer to numeral classifiers, which are used with nouns that are countable in some languages.

Informally, such Brachyceran larvae are called maggots, but the term is nontechnical and often applied indifferently to fly larvae or insect larvae in general.

Informally listed places are:

Informally, this means that arguments of this form do not give good reason to establish their conclusions, even if their premises are true.

Informally, a set of natural numbers A is Turing reducible to a set B if there is an oracle machine that correctly tells whether numbers are in A when run with B as the oracle set ( in this case, the set A is also said to be ( relatively ) computable from B and recursive in B ).

Informally, the reconstruction conjecture in graph theory says that graphs are determined uniquely by their subgraphs.

Informally, senators are sometimes given the higher title of ' Venerable '.

Informally, the terms C standard library or C library or libc are also used to designate a particular implementation on a given system.

Informally, this means that differentiable functions are very atypical among continuous functions.

Informally, a free object over a set A can be thought as being a " generic " algebraic structure over A: the only equations that hold between elements of the free object are those that follow from the defining axioms of the algebraic structure.

Informally, subvarieties are in general position if they cannot be described more simply than others.

Informally, two sets are close in the Hausdorff distance if every point of either set is close to some point of the other set.

Informally, two crystals tend to be in the same crystal system if they have similar symmetries, though there are many exceptions to this.

Informally, given the prime factorization of m, take b to be the product of the prime factors of m that have an odd exponent ( if there are none, then take b to be 1 ).

Informally, medical graduates are called " Doctors.

Informally, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.

Informally the Church – Turing thesis states that if some method ( algorithm ) exists to carry out a calculation, then the same calculation can also be carried out by a Turing machine ( as well as by a recursively definable function, and by a λ-function ).

Informally the word is also used to describe a procedure or process with a specific purpose.

Informally the name also refers to a larger district, the Monte Carlo Quarter ( corresponding to the former municipality of Monte Carlo ), which besides Monte Carlo / Spélagues also includes the wards of La Rousse / Saint Roman, Larvotto / Bas Moulins, and Saint Michel.

Informally, free abelian groups or formal sums may also be seen as signed multisets with elements in B.

Informally, this nation was also simply known as Germany.

Informally, the novels compose The Forever War series ; the novel also inspired a comic book and a board game.

Informally, Indonesians also use the word " perak " (' silver ' in Indonesian ) in referring to rupiah.

Informally, asphalt concrete is also referred to as " blacktop ", particularly in North America.

Informally, software developers may also use zeroise to mean any overwriting of sensitive data, not necessarily of a cryptographic nature.

Informally, it is still also known as ARD among viewers.

Informally, this type of graph is a set of objects called vertices ( or nodes ) connected by links called edges ( or arcs ), which can also have associated directions.

Informally, this reads as follows: something exists with the property F, there is only one such thing, and this unique thing also has the property G.

Informally, to estimate the area of a domain D, first pick a simple domain E whose area is easily calculated and which contains D. Now pick a sequence of random points that fall within E. Some fraction of these points will also fall within D. The area of D is then estimated as this fraction multiplied by the area of E.

Informally called " fudging the data ," this practice includes selective reporting ( see also publication bias ) and even simply making up false data.

Informally, other members of the higher hierarchic echelons of the Catholic Church are in recent times also occasionally called " Princes of the church ", in which case this title may occasionally carry ironic connotations.

Informally, the Houston Cougars have also been referred to as the Coogs, UH, or simply Houston.

Informally, it says that all sufficiently long words in a regular language may be pumped — that is, have a middle section of the word repeated an arbitrary number of times — to produce a new word which also lies within the same language.

Informally called " Tu Canal " ( Your Channel ), the channel can also be seen in most parts of the San Diego market.

Informally, the market spilled into the surrounding neighborhood, both in terms of street vendors and in terms of the nearby Magazin Universal (" Universal Store ") named Bucur Obor, a large commercial building that has been parcelled up into hundreds of small, independent retail stores.

Informally known as " The Country Club of the South ," Furman was named one of the 362 most beautiful places in America by the American Society of Landscape Architects.