We first define a function b{t} as follows: given the set of squares such that each has three corners on C and vertex at t, b{t} is the corresponding set of positive parametric differences between T and the backward corner points.

We define these values as Af, and define g{t} in the same way for each T.

Articles of faith are sets of beliefs usually found in creeds, sometimes numbered, and often beginning with " We believe ...", which attempt to more or less define the fundamental theology of a given religion, and especially in the Christian Church.

We then define f ( x, y ) to be this z.

We can then define the differential map d: C < sup >∞</ sup >( M ) → T < sub > x </ sub >< sup >*</ sup > M at a point x as the map which sends f to df < sub > x </ sub >.

We can now define the value

We should not define ' wisdom ' as the absence of folly, or a healthy thing as whatever is not sick.

We cannot define a point except as ' something with no parts ', nor blindness except as ' the absence of sight in a creature that is normally sighted '.

We define the periodic Bernoulli functions P < sub > n </ sub > by

We then define a contravariant functor F from C to D as a mapping that

We need a " mark " to define where we are and which direction we are heading to see if we ever get back to exactly the same pixel.

Verner wrote, " We can conclude that although the ancient Egyptians could not precisely define the value of π, in practice they used it ".

We define the kernel of h to be the set of elements in G which are mapped to the identity in H

We define the degree of to be the number of universal quantifier blocks, separated by existential quantifier blocks as shown above, in the prefix of.

We define the inverse limit of the inverse system (( A < sub > i </ sub >)< sub > i ∈ I </ sub >, ( f < sub > ij </ sub >)< sub > i ≤ j ∈ I </ sub >) as a particular subgroup of the direct product of the A < sub > i </ sub >' s:

We wish to maximize total value subject to the constraint that total weight is less than or equal to W. Then for each w ≤ W, define m to be the maximum value that can be attained with total weight less than or equal to w. m then is the solution to the problem.

We could also define a Lie algebra structure on T < sub > e </ sub > using right invariant vector fields instead of left invariant vector fields.

* We then define truth-functional operators, beginning with negation.

We can define addition, subtraction, and multiplication on by the following rules:

We can define methods to manipulate these new complex types.

We assume that A is an m-by-n matrix over either the real numbers or the complex numbers, and we define the linear map f by f ( x ) = Ax as above.

We can define a multiplication on the set S using the Steiner triple system by setting aa

We may define a possibly different topology on X using the continuous ( or topological ) dual space X < sup >*</ sup >.

We can also define it as a second component of business which includes all activities, functions and institutions involved in transferring goods from producers to consumer.

We are trying to study a linear operator T on the finite-dimensional space V, by decomposing T into a direct sum of operators which are in some sense elementary.

We know from other references that Euclid ’ s was not the first elementary geometry textbook, but it was so much superior that the others fell into disuse and were lost.

We would expect to find the total probability by multiplying the probabilities of each of the actions, for any chosen positions of E and F. We then, using rule a ) above, have to add up all these probabilities for all the alternatives for E and F. ( This is not elementary in practice, and involves integration.

In 2008, Gibbons suggested that the Nevada legislature cut the state budget for elementary, secondary and higher education by 14 %., Las Vegas Sun .</ ref > Jim Rogers, Nevada Chancellor for Education, said of the budget cuts, " We ’ re talking about something that is going to cripple us financially and competitively.

" Beam me up, Scotty " is similar to the phrase, " Just the facts, ma ' am ", attributed to Jack Webb's character of Joe Friday on Dragnet, " It's elementary, my dear Watson ", attributed to Sherlock Holmes, " Luke, I am your father ", attributed to Darth Vader, or " Play it again, Sam ", attributed to Humphrey Bogart's character in Casablanca and " We don't need no stinkin ' badges!

We start in elementary school and he tells us his experiences.

Muhammad Zakariya Kandhalvi said, " We studied elementary Persian from him those days.

Education Center for students and teachers, sponsoring the " We the People " program promoting the understanding of civics for upper elementary and secondary students, along with national and state programs for teachers, such as the National Advanced Content Seminars, which focuses on historical content and teaching methods.

We have a language where is a constant symbol and is a unary function and the following axioms:

We now consider how the choice of description language affects the value of K, and show that the effect of changing the description language is bounded.

Likewise, Oscar Wilde wrote, " We have really everything in common with America nowadays, except, of course, the language " ( The Canterville Ghost, 1888 ).

For example, if I say “ Star Wars is a shitty movie ,” and my friend says, “ Star Wars is not a shitty movie !” We have no shared reality, for in our language, truth lies in only one of our statements and we can forever argue these truths until one of us writes a book and has more authority than the other.

:" We worship ," replied Hengist, " our country gods, Saturn and Jupiter, and the other deities that govern the world, but especially Mercury, whom in our language we call Woden and to whom our ancestors consecrated the fourth day of the week, still called after his name Wodensday.

A Karaim of Trakai talking in Karaim language in a documentary says We, descendants of Khazars of Kipchaks, came to Lithuania from Crimea long time ago.

In Metaphors We Live By George Lakoff and Mark Johnson argue that metaphors are pervasive in everyday life, not just in language, but also in thought and action.

We know this document only from a copy prepared by an anonymous monk who was not familiar with Polish language or Polish names.

We are now controlled not by binding extra-linguistic value paradigms defining notions of collective identity and ultimate purpose, but rather by our automatic responses to different species of " language games " ( a concept Lyotard imports from JL Austin's theory of Speech Acts ).

" We were actually trying to build something complicated and discovered, serendipitously, that we had accidentally designed something that met all our goals but was much simpler than we had intended .... we realized that the lambda calculus — a small, simple formalism — could serve as the core of a powerful and expressive programming language.

* We cannot say with language what is common in the structures, rather it must be shown, because any language we use will also rely on this relationship, and so we cannot step out of our language with language.

We might suppose we have a better conception of what minds are, because we are all ( the private language argument notwithstanding ) intimately acquainted with our own minds.

We repeat, then, in the light of this recapitulation of events, almost too recent to be called history, but which are familiar to us all, and on the most casual examination of the language of these amendments, no one can fail to be impressed with the one pervading purpose found in them all, lying at the foundation of each, and without which none of them would have been even suggested ; we mean the freedom of the slave race, the security and firm establishment of that freedom, and the protection of the newly made freeman and citizen from the oppressions of those who had formerly exercised unlimited dominion over him.

According to Theodore Roosevelt: " We have taken into our language the word prairie, because when our backwoodsmen first reached the land the Midwest and saw the great natural meadows of long grass — sights unknown to the gloomy forests wherein they had always dwelt — they knew not what to call them, and borrowed the term already in use among the French inhabitants.

In George Lakoff and Mark Johnson ’ s work, Metaphors We Live By ( 1980 ), we see how everyday language is filled with metaphors we may not always notice.

:: Example: We have consistently applied that presumption to language in the ADEA that was " derived in haec verba from Title VII.

As the masterbrain behind this experiment, Lord Palafox, says in chapter 9: " We must alter the mental framework of the Paonese people, which is most easily achieved by altering the language.

We need to give a clear definition to our language ... We know that ebony means black and that phonics refers to speech sounds or the science of sounds.

We consider two such regular expressions equal if they describe the same language.

Stelios Papadimitriou, president of the foundation, has remarked: " We are not going to turn the Onassis Foundation over to someone who has no connection with our culture, our religion, our language or our shared experiences, and who never went to college or worked a day in her life.