They appear in virtually every branch of modern mathematics and are a central unifying notion.

It explores the notion that " Islam is the only synthesis capable of unifying mankind's essentially dualistic existence ".

On the political side, King rejected any notion of a government of national unity.

The manifesto thus combined elements of contemporary democratic and progressive thought ( franchise reform, labour reform, limited nationalisation, taxes on wealth and war profits ) with corporatist emphasis on class collaboration ( the idea of social classes existing side by side and collaborating for the sake of national interests ; the opposite of the Marxist notion of class struggle ).

Even the contemporary notion of " two Serbia's "— one supposedly national, liberal and Eurocentric, and the other conservative, nationalist and Euroskeptic — seems to be the extension of the said discord.

While the notion of needing to remove alien influences to reconstruct Latvian traditions was preserved into later times, the attempts to create an Olympus-like pantheon of pseudo-gods eventually stopped as national romanticism was replaced by realism and came to be criticized in the first half of 20th century.

The sociological notion of identity, by contrast, has to do with a person's self-conception, social presentation, and more generally, the aspects of a person that make them unique, or qualitatively different from others ( e. g. cultural identity, gender identity, national Identity, online identity and processes of identity formation.

According to Ellwood, the part of Eliade that felt attracted to the " freedom of new beginnings suggested by primal myths " is the same part that felt attracted to the Guard, with its almost mythological notion of a new beginning through a " national resurrection ".

Especially after the technology boom of the 1980s, both sides of the aisle have generally embraced the notion that government-funded basic research is essential for the nation's economic health and global competitiveness, as well as for the national defense.

The Beruf unserer Zeit, in addition to the more specific object the treatise had in view, which has been already treated, expresses the idea, unfamiliar in 1814, that law is part and parcel of national life, and combats the notion, too much assumed by French jurists, especially in the 18th century, and countenanced in practice by Bentham, that law might be arbitrarily imposed on a country irrespective of its state of civilization and history.

Thus, nationalism is invoked in conscience to quell tribal conflict and the notion of a Brotherhood of Man is invoked to quell national conflicts.

The common theme to his first and last political works is the notion of a national policy ( Kokutai ), through which Japan would lead a united and free Asia ( see pan-Asianism ).

As early as 1870, Syrian writer Francis Marrash distinguished the notion of fatherland from that of nation ; when applying the latter to Greater Syria, he pointed to the role played by language, besides customs and belief in common interests, in defining national identity.

Croat national identity was adopted by some Bunjevci in the late 19th and early 20th century, especially by the majority of the Bunjevac clergy, notably one of the titular bishops of Kalocsa Ivan Antunović ( 1815 – 1888 ) supported the notion of calling Bunjevci and Šokci with the name Croats.

Thinley blamed the global economic crisis of 2008 – 2009 on " insatiable human greed " and stressed the need to instead focus on the Bhutanese notion of gross national happiness.

University of Notre Dame professor John McGreevy defines it as " the notion that national customs might trump Roman ( Catholic Church ) regulations.

The immigrants were inspired by the notion of creating a national home for Jews.

This notion of Turkish youth struggling with national identity is perhaps most clearly addressed by Cartel ’ s lyrical content.

Plans for a national home and away league went back as far as 1965 for a 1967 start, and were followed up by variations on the theme throughout the 1960s and early 1970s, but faced opposition variously from clubs, who deemed the notion uneconomical, and state federations who feared losing their power.

" The notion of a pro-slavery invasion by the U. S. was rejected in light of the newly ignited controversy over the Kansas – Nebraska Act, so a purchase or intervention in the name of national security was deemed the most acceptable method of acquisition.

The core notion was that ‘ being, and being seen to be, a good international citizen ’ should be seen not as the ‘ foreign policy equivalent of boy-scout good deeds ’, but as a distinct component of any country ’ s national interest, ‘ quite distinct from the familiar duo of security and economic interests ’:

Contrary to the earlier descriptions of the two island groups as distinct entities, a 16th century notion relegates Antillia to the island of São Miguel, the largest of the Azores, where a national park centering on two lakes still bears the name Sete Cidades.

Déat replaced class struggle by collaboration of classes and national solidarity, advocated corporatism as a social organization model, replaced the notion of " Socialism " by " anti-Capitalism " and supported an authoritarian state which would plan the economy and from which parliamentarism would be repealed.

Hirsh states " to speak of as genocidal in a context of religious competition and conflict risks diluting the notion of genocide and equating it with any conflict between national, religious, or racial groups ".

Déat replaced class struggle by collaboration of classes and national solidarity, advocated corporatism as a social organization model, replaced the notion of " Socialism " by " anti-Capitalism " and supported an authoritarian state which would plan the economy and from which parliamentarism would be repealed.

Dwight D. Eisenhower criticized the notion of the confluence of corporate power and de facto fascism, but nevertheless brought attention to the " conjunction of an immense military establishment and a large arms industry " in his 1961 Farewell Address to the Nation, and stressed " the need to maintain balance in and among national programs -- balance between the private and the public economy, balance between cost and hoped for advantage.

The notion of a static unchanging Form and its identity with Substance represents the metaphysical view that has come to be held as an assumption by the vast majority of the Western philosophical tradition since Plato and Aristotle, as it was something they agreed on.

A key notion in the work of the Frankfurt School since Dialectic of Enlightenment had been the idea of thought becoming an instrument of domination that subsumes all objects under the control of the ( dominant ) subject, especially through the notion of identity, i. e. of identifying as real in nature and society only that which harmonized or fit with dominant concepts, and regarding as unreal or non-existent everything that did not.

The definition in the previous section generalizes the notion of inverse in group relative to the notion of identity.

It's also possible, albeit less obvious, to generalize the notion of an inverse by dropping the identity element but keeping associativity, i. e. in a semigroup.

This is generally justified because in most applications ( e. g. all examples in this article ) associativity holds, which makes this notion a generalization of the left / right inverse relative to an identity.

The idea of being the " freest " or " most general " algebra subject to this identity can be formally expressed through the notion of a universal property, as done below.

Fellow reductionist Mark Johnston of Princeton rejects Parfit's constitutive notion of identity with what he calls an " Argument from Above ".

For example, some LGBT youth become aware of and accept their same-sex desires or gender identity at puberty in a way similar to which heterosexual teens become aware of their sexuality, i. e. free of any notion of difference, stigma or shame in terms of the gender of the people to whom they are attracted.

The notion of identity gives rise to many philosophical problems, including the identity of indiscernibles ( if x and y share all their properties, are they one and the same thing?

It is important to distinguish the philosophical concept of identity from the more well-known notion of identity in use in psychology and the social sciences.

" More recent metaphysicians have discussed trans-world identity — the notion that there can be the same object in different possible worlds.

Richard arrived at the result that the notion of identity of two objects and the invariability of an object are too vague and need to be specified more precisely.

* Axioms are propositions, the task of which is to make precise the notion of identity of two objects pre-existing in our mind.

Ethnicity theorists embraced an individualist, quasi-voluntarist notion of identity, which downplayed the significance of race as structuring element in US history and society.

The notion that an ordinary category must have identity morphisms is replaced by the second and third diagrams, which express identity in terms of left and right unitors: