* Klal ufrat, a generality and a particularity: If we find a phrase signifying a particularity following that of a generality, the particularity particularises the generality and we only take that particular case into account.

* Klal shehu tzarich lifrat, a generality that requires a particularity, and a particularity that requires a generality: If it is impossible to have the more general law without more specific examples or more specific cases without the statement of the general law, the above three rules don't apply.

He answered that since the Bnei Reuven had been distant from the rest of Klal Yisroel before this ruling had been accepted, there is no reason to assume that they accepted this ruling, and there was a chance that they were still keeping the institution of semikhah alive.

It is not well known, but the work is actually not a commentary on the Talmud but is rather a commentary on the Rif, and always starts with the text of the Rif ( see Shach quoted in Kellolei HoRif, Rabbeinu Osher, ViTur printed before the Rosh on Shabbos, Klal 2 ).

80 is the value of Klal ( כלל ), the " community ", the extension of Kol ( כל ), the term in Kabbalah for the sephirah of Yesod.

: Years ago, an organization like the Chofetz Chaim Heritage Foundation -- which is marshaling the latest technology and enlisting the best communicators to help Klal Yisroel fight loshon hara and other sins of speech – would have been unimaginable.

:... Reform, Conservative and Reconstructionist communities are not only more numerous in their official memberships than the Orthodox community, but they are also vital, powerful and dynamic ; they are committed to Jewish survival, each according to its own lights ; they are a part of Klal Yisrael ; and they consider their rabbis their leaders.

) What a great zechus ( merit ) this would be for Klal Yisrael during these perilous times if thousands of Jews become more careful in guarding their speech.

In this way, the school strengthens and energizes Conservative Judaism and Klal Yisrael.

* Prat ukhlal, a particularity and a generality: If the order is first the particularity and then the generality, we add from the generality upon the particularity, even to a broad extent.

If this is not already the case then both A and B can be multiplied by this factor ; the factor cancels so the terms are unchanged and there is no loss of generality.

* Pre-Test Effects: If cause-effect relationships can only be found when pre-tests are carried out, then this also limits the generality of the findings.

* Post-Test Effects: If cause-effect relationships can only be found when post-tests are carried out, then this also limits the generality of the findings.

As explained in the section Equivalence with function problems below, there is no loss of generality.

Using Rogers ' characterization of acceptable programming systems, Rice's Theorem may essentially be generalized from Turing machines to most computer programming languages: there exists no automatic method that decides with generality non-trivial questions on the black-box behavior of computer programs.

However, this is a generality ; in many states, there are villages that are an order of magnitude larger than the smallest cities in the state.

At the head of a generality was an intendant, but in the case of Languedoc there was only one intendant responsible for both generalities, and he was often referred to as the intendant of Languedoc, even though technically speaking he was in fact the intendant of the generality of Toulouse and intendant of the generality of Montpellier.

For generality, assume there are ( say ) N such symmetry transformations of the action, i. e. transformations leaving the action unchanged ; labelled by an index r = 1, 2, 3, …, N.

This calculation can be carried out more easily if one first observes that ( by scaling ) there is no loss of generality in assuming that and.

Thus, originalists often conceal their choice between levels of generality or possible alternative meanings as required by the original meaning when there is considerable room for disagreement.

Even without knowledge that we are working in the multiplicative group of integers modulo n, we can show that a actually has an order by noting that the powers of a can only take a finite number of different values modulo n, so according to the pigeonhole principle there must be two powers, say s and t and without loss of generality s > t, such that a < sup > s </ sup > ≡ a < sup > t </ sup > ( mod n ).

And there are stock phrases in mathematics, used with specific meanings, such as " if and only if ", " necessary and sufficient " and " without loss of generality ".

The class of Polish spaces has several universality properties, which show that there is no loss of generality in considering Polish spaces of certain restricted forms.

Therefore, there is no loss of generality, if we restrict our data structure to the case of monotone subdivisions, as we do in this section.

With the development of homology theory to include K-theory and other extraordinary theories from about 1955, it was realised that the homology H < sub >*</ sub > could be replaced by other theories, once the products on manifolds were constructed ; and there are now textbook treatments in generality.

Without loss of generality, let there exist a function such that

The missing numbers can be assumed as " 0 ", so there is no loss of generality.

The introduction of quantification, needed to solve the problem of multiple generality, rendered impossible the kind of subject-predicate analysis that governed Aristotle's account, although there is a renewed interest in term logic, attempting to find calculi in the spirit of Aristotle's syllogistic but with the generality of modern logics based on the quantifier.

Although the long-term population persistence of several species with low genetic variation has recently prompted debate on the generality of inbreeding depression, there are various empirical evidences for genetic Allee effects.

Note that there must then be two distinct factors of length 1, implying that word uses exactly 2 symbols from the alphabet ( without loss of generality we can call these 0 and 1 ).

In more generality, if there is an monomial matrix which sends C < sub > 1 </ sub > isomorphically to C < sub > 2 </ sub > then we say C < sub > 1 </ sub > and C < sub > 2 </ sub > are equivalent.

The impression was unmistakable that, whatever one may choose to call it, natural law is a functioning generality with a certain objective existence.

no necessary assumptions for ANOVA is its full generality, but the

Continuity of functions is one of the core concepts of topology, which is treated in full generality below.

What we have constructed is called the Alexandroff one-point compactification of the real line, discussed in more generality below.

In more generality, reflection across a line through the origin making an angle with the x-axis, is equivalent to replacing every point with coordinates ( x, y ) by the point with coordinates ( x < nowiki >'</ nowiki >, y < nowiki >'</ nowiki >), where

* Deductive reasoning, inference in which the conclusion is of no greater generality than the premises

So it suffices to prove the four color theorem for triangulated graphs to prove it for all planar graphs, and without loss of generality we assume the graph is triangulated.

Pan ( 1986 ) proved an lower bound assuming a bound on a measure of the FFT algorithm's " asynchronicity ", but the generality of this assumption is unclear.

Another of the most common objections to reliabilism, made first to Goldman's reliable process theory of knowledge and later to other reliabilist theories, is the so-called generality problem.

We can assume without loss of generality that the support of each X < sub > i </ sub > is

Multilinear algebra can be developed in greater generality than for scalars coming from a field, but the theory is then certainly less geometric, and computations more technical and less algorithmic.

As with every universal property, the above definition describes a balanced state of generality: The limit object L has to be general enough to allow any other cone to factor through it ; on the other hand, L has to be sufficiently specific, so that only one such factorization is possible for every cone.

While that glittering generality has rhetorical appeal, it is not a correct statement of the law.

Since y ( t ) is the derivate of x ( t ) we can without loss of generality rewrite it as

where the origin of the z-axis is defined, without loss of generality, to coincide with the beam waist, and where

There is a school of thought among economic historians that splits economic history — the study of how economic phenomena evolved in the past — from historical economics — testing the generality of economic theory using historical episodes.