For one thing, there is a natural belt of rock across the river bed ; ;

For the only time in the opera, words are not set according to their natural inflection ; ;

For so long as death was not violent, it was natural and to be welcomed, making a funeral a feast.

For the Aztec the count by 20s was completely natural.

For example, Pyrethrum ( refers to several Old World plants of the genus Chrysanthemum ) is a natural insecticide with minimal environmental impact.

For example, suppose that each member of the collection X is a nonempty subset of the natural numbers.

For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.

For example, the positrons produced in natural radioactive decay quickly annihilate themselves with electrons, producing pairs of gamma rays, a process exploited in positron emission tomography.

For Hume, philosophy can be split into two general parts: natural philosophy and the philosophy of human nature ( or, as he calls it, " moral philosophy ").

For most of human history, pearls were the ultimate precious beads of natural origin because of their rarity, although the pearl-culturing process has now made them far more common.

For example, the division example above is surjective ( or onto ) because every rational number may be expressed as a quotient of an integer and a natural number.

For example, the division example above may also be interpreted as a partial binary function from Z and N to Q, where N is the set of all natural numbers, including zero.

For natural numbers ( taken to include 0 ) n and k, the binomial coefficient can be defined as the coefficient of the monomial X < sup > k </ sup > in the expansion of.

Some sets are infinite ; these sets have more than n elements for any integer n. For example, the set of natural numbers, denotable by, has infinitely many elements, and we cannot use any normal number to give its size.

For example, Georg Cantor ( who introduced this concept ) demonstrated that the real numbers cannot be put into one-to-one correspondence with the natural numbers ( non-negative integers ), and therefore that the set of real numbers has a greater cardinality than the set of natural numbers.

* For every natural number, the-sphere is compact.

For each specific consistent effectively represented axiomatic system for the natural numbers, such as Peano arithmetic, there exists a constant N such that no bit of Ω after the Nth can be proven to be one or zero within that system.

For example, the cofinality of ω² is ω, because the sequence ω · m ( where m ranges over the natural numbers ) tends to ω² ; but, more generally, any countable limit ordinal has cofinality ω.

For this reason, its practice violated the natural laws of medicine, transforming health care practitioners into those who harm rather than heal.

For example, by inoculating in the months of milder climate, one had a better chance of fighting the infection and becoming immune instead of the alternative: natural exposure to the disease during harsher weather, when the body's defenses were already challenged.

For example, philosopher John D. Kenyon writes: Reason might manage to raise a doubt about the truth of a conclusion of natural inductive inference just for a moment in the study, but the forces of nature will soon overcome that artificial skepticism, and the sheer agreeableness of animal faith will protect us from excessive caution and sterile suspension of belief.

For instance, we could define natural number as follows ( after Peano ):

For example, Darwinism may be used to refer to Darwin's proposed mechanism of natural selection, in comparison to more recent mechanisms such as genetic drift and gene flow.

For example, while burning an area of fairly thick forest and thus turning it into a more open, grassy environment might reduce the viability of a large browser ( an animal that eats leaves and shoots rather than grasses ), the reverse could also be true: removing the browsing animals ( by eating them, or by any other means ) within a few years produces a very thick undergrowth which, when a fire eventually starts through natural causes ( as fires tend to do every few hundred years ), burns with greater than usual ferocity.

For the low-temperature measurements the sample was cooled by a cold nitrogen gas flow method similar to that of Andrew and Eades.

For in a world as yet unacquainted with the horrors of the mushroom cloud, poison gas was still regarded as the ultimate in hideous weapons.

For a monatomic ideal gas,, and for a diatomic gas ( such as nitrogen and oxygen, the main components of air ).

For an adiabatic free expansion of an ideal gas, the gas is contained in an insulated container and then allowed to expand in a vacuum.

For an ideal gas, the temperature remains constant because the internal energy only depends on temperature in that case.

For an ideal gas the internal energy is given by

For example, gas chromatography-mass spectrometry, gas chromatography-infrared spectroscopy, liquid chromatography-mass spectrometry, liquid chromatography-NMR spectroscopy.

For field ion microscopy a gas is introduced, known as the imaging gas, into the chamber at very low pressures.

For example, an increase in pressure due to decreasing volume causes the reaction to shift to the side with the fewer moles of gas.

For example, simple hydrogen gas combined with simple oxygen gas can produce a more complex substance, such as water.

For determining the density of a liquid or a gas, a hydrometer or dasymeter may be used, respectively.

For an ideal gas the partial pressure is related to the molar concentration by the relation

For example, scientific uncertainty fuels the ongoing debate over greenhouse gas regulation and is a major factor in the debate over whether to ban pesticides.

For example, to synthesize iso-octane ( the 8-carbon ideal gasoline ) from the unfunctionalized alkane isobutane ( a 4-carbon gas ), isobutane is first dehydrogenated into isobutene.

For example, " brake fluid " is hydraulic oil and will not perform its required function if there is gas in it.

For high energy gamma, this relies on interaction of the photon radiation with the tube wall material, usually 1-2mm of chrome steel to produce electrons which can enter and ionise the fill gas.

For this helium conservation program, the Bureau built a pipeline from Bushton, Kansas, to connect those plants with the government's partially depleted Cliffside gas field, near Amarillo, Texas.

For example, unlike when handloading rifle and pistol cartridges, where all the various components ( cases, gas checks, powder, primers, etc.

For example, if a liquid or gas contains ions, then the ions can be made to flow as an electric current, and the material is a conductor.

For this reason, the semiconductor fabrication facilities are highly automated, and may feature negative pressure gas bottles safe delivery system ( SDS ).