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...]]. For later reference, it will also be useful to see the divergence on a fundamental level. By definition, the convergence or divergence of an infinite series i ...+ 4 + · · ·|1 + 2 + 3 + 4 + …]]}}, which has deep applications in modern [[physics]] but requires much stronger methods to sum. ...

...creator of [[set theory]], which has become a [[foundations of mathematics|fundamental theory]] in mathematics. Cantor established the importance of [[one-to-one ...and provides a standard set of axioms to prove or disprove them. The basic concepts of set theory are now used throughout mathematics. ...

...s. [[Matrix group]]s, for example, can be used to understand fundamental [[physics|physical]] laws underlying [[special relativity]] and symmetry phenomena in == Basic concepts == ...

...{pron-en|kwɔrk}} or {{IPA-en|kwɑrk|}}) is an [[elementary particle]] and a fundamental constituent of [[matter]]. Quarks combine to form [[composite particle]]s c |publisher=[[Georgia State University]], Department of Physics and Astronomy ...

...be reconciled with the laws of [[Introduction to quantum mechanics|quantum physics]] to produce a complete and self-consistent theory of [[quantum gravity]]. ...y introduced a new framework for all of physics by proposing radically new concepts of [[space]] and [[time]]. Some then-accepted physical theories were incon ...

...ofs does not have to be taken on faith or as an axiom; it follows from the fundamental relationship between decimals and the numbers they represent. This relation The Nested Intervals Theorem is usually founded upon a more fundamental characteristic of the real numbers: the existence of [[least upper bound]]s ...

| caption = Photons emitted in a [[Coherence (physics)|coherent]] beam from a [[laser]] ...scopic]] level, because the photon has no [[rest mass]]; this allows for [[fundamental interaction|interaction]]s at long distances. Like all elementary particles ...

| fields = [[Mathematics]] and [[Physics]] | known_for = [[Abstract algebra]]<br />[[Theoretical physics]] ...

...rn [[number theory]], such as [[Lagrange's four-square theorem]] and the [[fundamental theorem of arithmetic]] (unique factorization). ...16.</ref> although the latter notation is also used for other mathematical concepts, such as two-dimensional [[coordinate vector|vectors]]. ...

...yed making the trip to St Petersburg while he unsuccessfully applied for a physics professorship at the University of Basel.<ref name="stpetersburg">{{cite jo ...er swiftly rose through the ranks in the academy and was made professor of physics in 1731. Two years later, Daniel Bernoulli, who was fed up with the censors ...

..., and describes gravity as a geometric property of [[space]] and [[Time in physics|time]], or [[spacetime]]. In particular, the [[curvature]] of spacetime is ...relativity can be reconciled with the laws of [[quantum mechanics|quantum physics]] to produce a complete and self-consistent theory of [[quantum gravity]]. ...

...he smallest indivisible particle of matter". Although the Indian and Greek concepts of the atom were based purely on philosophy, modern science has retained th | url=http://nobelprize.org/nobel_prizes/physics/laureates/1906/thomson-bio.html ...

...s forms; for example, the average [[kinetic energy]] in the [[translation (physics)|translational motion]] of a molecule should equal the average kinetic ener ...namic) temperature]]. More generally, it can be applied to any [[classical physics|classical system]] in [[thermal equilibrium]], no matter how complicated. T ...

...eneral relativity]] and on simplifying assumptions (such as [[homogeneity (physics)#Translation invariance|homogeneity]] and [[isotropy]] of space). The gover ...se accelerators have limited capabilities to probe into such [[high-energy physics|high energy regimes]]. Without any evidence associated with the earliest in ...

...cating life; and finally the expected lifetimes of such civilizations. The fundamental problem is that the last four terms (fraction of planets with life, odds li ...ollider#Fears among the public|example of fears of civilization destroying physics experiments]]. This particular fear (particle colliders creating black hol ...