natural numbers

(noun)

A set of numbers sometimes described as all non-negative integers $(0, 1, 2, ...)$ and sometimes described as all positive integers $(1, 2, 3, ...)$.

Related Terms

Examples of natural numbers in the following topics:

  • The Number e

    • The number $e$ is an important mathematical constant, approximately equal to $2.71828$.
    • When used as the base for a logarithm, we call that logarithm the natural logarithm and write it as $\ln x$.
    • The number $e$, sometimes called the natural number, or Euler's number, is an important mathematical constant approximately equal to 2.71828.
    • When used as the base for a logarithm, the corresponding logarithm is called the natural logarithm, and is written as $\ln (x)$.
    • There are a number of different definitions of the number $e$.

  • Average Atomic Mass

    • The atomic number of an element defines the element's identity and signifies the number of protons in the nucleus of one atom.
    • For any given isotope, the sum of the numbers of protons and neutrons in the nucleus is called the mass number.
    • Average atomic mass = f1M1 + f2M2 + ... + fnMn where f is the fraction representing the natural abundance of the isotope and M is the mass number (weight) of the isotope.
    • Chlorine consists of two major isotopes, one with 18 neutrons (75.77 percent of natural chlorine atoms) and one with 20 neutrons (24.23 percent of natural chlorine atoms).
    • Then, calculate the mass numbers.

  • Carboxylic Acid Natural Products

    • Carboxylic acids are widespread in nature, often combined with other functional groups.
    • Interestingly, the molecules of most natural fatty acids have an even number of carbon atoms.
    • Analogous compounds composed of odd numbers of carbon atoms are perfectly stable and have been made synthetically.
    • Since nature makes these long-chain acids by linking together acetate units, it is not surprising that the carbon atoms composing the natural products are multiples of two.
    • The following formulas are examples of other naturally occurring carboxylic acids.

  • Atomic Number and Mass Number

    • The atomic number is the number of protons in an element, while the mass number is the number of protons plus the number of neutrons.
    • An element's mass number (A) is the sum of the number of protons and the number of neutrons.
    • Scientists determine the atomic mass by calculating the mean of the mass numbers for its naturally-occurring isotopes.
    • Given an atomic number (Z) and mass number (A), you can find the number of protons, neutrons, and electrons in a neutral atom.
    • Determine the relationship between the mass number of an atom, its atomic number, its atomic mass, and its number of subatomic particles

  • Nuclear Stability

    • Of the 254 known stable nuclides, only four have both an odd number of protons and an odd number of neutrons:
    • Radionuclides occur naturally but can also be produced artificially.
    • All elements form a number of radionuclides, although the half-lives of many are so short that they are not observed in nature.
    • For every chemical element, many radioisotopes that do not occur in nature (due to short half-lives or the lack of a natural production source) have been produced artificially.
    • An atomic nucleus emits an alpha particle and thereby transforms ("decays") into an atom with a mass number smaller by four and an atomic number smaller by two.

  • Poisson Distribution

    • The Poisson distribution can be used to calculate the probabilities of various numbers of "successes" based on the mean number of successes.
    • Suppose you knew that the mean number of calls to a fire station on a weekday is 8.

  • Natural Logarithms

    • The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number.
    • The natural logarithm is the logarithm with base equal to e.
    • The natural logarithm can be written as $\log_e x$ but is usually written as $\ln x$.
    • Just as the exponential function with base $e$ arises naturally in many calculus contexts, the natural logarithm, which is the inverse function of the exponential with base $e$, also arises in naturally in many contexts.
    • The first step is to take the natural logarithm of both sides:

  • Natural Monopolies

    • A natural monopoly's cost structure is very different from that of most industries.
    • Natural monopolies tend to form in industries where there are high fixed costs.
    • A firm with high fixed costs requires a large number of customers in order to have a meaningful return on investment.
    • As it gains market share and increases its output, the fixed cost is divided among a larger number of customers.
    • Examples of natural monopolies are water and electricity services.

  • Special Considerations for Acquisition and Depletion of Natural Resources

    • Resources supplied by nature, such as ore deposits, mineral deposits, oil reserves, gas deposits, and timberstands, are natural resources or wasting assets.
    • In each accounting period, the depletion recognized is an estimate of the cost of the natural resource that was removed from its natural setting during the period.
    • Then assign this total cost to either the cost of natural resources sold or the inventory of the natural resource still on hand.
    • They divide total cost by the estimated number of units–tons, barrels, or board feet–that can be economically extracted from the property.
    • Define a natural resource and how to properly account for its depletion

  • Charles Darwin and Natural Selection

    • During a period in which rainfall was higher than normal because of an El Niño, the large hard seeds that large-billed birds ate were reduced in number; however, there was an abundance of the small soft seeds which the small-billed birds ate.
    • Darwin called this mechanism natural selection.
    • Natural selection, Darwin argued, was an inevitable outcome of three principles that operated in nature.
    • The capacity for reproduction in all organisms outstrips the availability of resources to support their numbers.
    • His book outlined his arguments for evolution by natural selection.