“When… we have a series of values of a quantity which continually diminish, and in such a way, that name any quantity we may, however small, all the values, after a certain value, are severally less than that quantity, then the symbol by which the values are denoted is said to diminish without limit. And if the series of values increase in succession, so that name any quantity we may, however great, all after a certain point will be greater, then the series is said to increase without limit. It is also frequently said, when a quantity diminishes without limit, that it has nothing, zero or 0, for its limit: and that when it increases without limit it has infinity or ∞ or 1⁄0 for its limit.”

— Augustus De Morgan

Introductory Chapter, pp.9-10
The Differential and Integral Calculus (1836)

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "When… we have a series of values of a quantity which continually diminish, and in such a way, that name any quantity we…" by Augustus De Morgan?

Augustus De Morgan 41

British mathematician, philosopher and university teacher (… 1806–1871

Related quotes

“When… we have a series of values of a quantity which continually diminish, and in such a way, that name any quantity we may, however small, all the values, after a certain value, are severally less than that quantity, then the symbol by which the values are denoted is said to diminish without limit. And if the series of values increase in succession, so that name any quantity we may, however great, all after a certain point will be greater, then the series is said to increase without limit.”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

It is also frequently said, when a quantity diminishes without limit, that it has nothing, zero or 0, for its limit: and that when it increases without limit it has infinity or ∞ or 1&frasl;0 for its limit.
The Differential and Integral Calculus (1836)

“The following is exactly what we mean by a LIMIT. …let the several values of x… bea1 a2 a3 a4.... &c.;then if by passing from a1 to a2, from a2 to a3, &c.;, we continually approach to a certain quantity l [lower case L, for "limit"], so that each of the set differs from l by less than its predecessors; and if, in addition to this, the approach to l is of such a kind, that name any quantity we may, however small, namely z, we shall at last come to a series beginning, say with an, and continuing ad infinitum,an an+1 an+2.... &c.;all the terms of which severally differ from l by less than z: then l is called the limit of x with respect to the supposition in question.”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

The Differential and Integral Calculus (1836)

“Knowledge is like money: To be of value it must circulate, and in circulating it can increase in quantity and, hopefully, in value.”

Louis L'Amour (1908–1988) Novelist, short story writer

Source: Education of a Wandering Man

“The potential infinite means nothing other than an undetermined, variable quantity, always remaining finite, which has to assume values that either become smaller than any finite limit no matter how small, or greater than any finite limit no matter how great.”

Georg Cantor (1845–1918) mathematician, inventor of set theory

"Mitteilungen" (1887-8)

“Rather, for all objects and experiences there is a quantity that has an optimum value. Above that quantity, the variable becomes toxic. To fall below that value is to be deprived.”

Gregory Bateson (1904–1980) English anthropologist, social scientist, linguist, visual anthropologist, semiotician and cyberneticist

Source: Mind and Nature: A Necessary Unity, 1979, p. 56

“Once the means of production have become capital, a certain quantity of value is augmented through the exploitation of labor. And this valorizing value is capital.”

Itsurō Sakisaka (1897–1985) Japanese economist

Exploitation of Labor (1967)

“We cannot diminish the value of one category of human life — the unborn — without diminishing the value of all human life.”

Ronald Reagan (1911–2004) American politician, 40th president of the United States (in office from 1981 to 1989)

1980s, First term of office (1981–1985), Abortion and the Conscience of the Nation (1983)

“Assuming… that all available goods of higher order are employed in the most economic fashion, the value of a concrete quantity of a good of higher order is equal to the difference in importance between the satisfactions that can be attained when we have command of the given quantity of the good of higher order whose value we wish to determine and the satisfactions that would be attained if we did not have this quantity at our command.”

Carl Menger (1840–1921) founder of the Austrian School of economics

Source: Principles,, p. 164-5; cited in: Randall G. Holcombe, Great Austrian Economists, p. 90

“Take a unit, halve it, halve the result, and so on continually. This gives—1 1⁄2 1⁄4 1⁄8 1⁄16 1⁄32 1⁄64 1⁄128 &c.;Add these together, beginning from the first, namely, add the first two, the first three, the first four, &c;… We see then a continual approach to 2, which is not reached, nor ever will be, for the deficit from 2 is always equal to the last term added.
…We say that—1, 1 + 1⁄2, 1 + 1⁄2 + 1⁄4, 1 + 1⁄2 + 1⁄4 + 1⁄8, &c.; &c.;is a series of quantities which continually approximate to the limit 2. Now the truth is, these several quantities are fixed, and do not approximate to 2. …it is we ourselves who approximate to 2, by passing from one to another. Similarly when we say, "let x be a quantity which continually approximates to the limit 2," we mean, let us assign different values to x, each nearer to 2 than the preceding, and following such a law that we shall, by continuing our steps sufficiently far, actually find a value for x which shall be as near to 2 as we please.”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

The Differential and Integral Calculus (1836)

“The value of money is in proportion to the quantity of the necessaries of life which it will purchase.”

Adam Smith (1723–1790) Scottish moral philosopher and political economist

Source: (1776), Book V, Chapter II, Part II, Article IV.

Help us to complete the source, original and additional information

Augustus De Morgan 41

Related quotes

Related topics