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 MorganRelated topics
certain great increase infinity less name nothing point series small value way zeroRelated quotes
"Heaven helps those who help themselves" is a well-tried maxim, embodying in a small compass the results of vast human experience. The spirit of self-help is the root of all genuine growth in the individual; and, exhibited in the lives of many, it constitutes the true source of national vigour and strength. Help from without is often enfeebling in its effects, but help from within invariably invigorates. Whatever is done for men or classes, to a certain extent takes away the stimulus and necessity of doing for themselves; and where men are subjected to over-guidance and over-government, the inevitable tendency is to render them comparatively helpless.
Samuel Smiles
...there is no point to musical analysis at all unless it is 'two-dimensional' – unless [...] one examines the music in terms of what I call its 'Background' (and this 'Background' is the sum total of the expectations which the composer creates) and its 'Foreground' (and its 'Foreground' is what he does instead). That is to say, the composer creates certain expectations, well-defined expectations, which he proceeds to meaningfully contradict. There is therefore a strong relation between 'Background' and 'Foreground', between that which happens and that which lies at its back – or to put it the other way round, between that which the composer leads you to expect, and that which he does instead...
Hans Keller
To the biologist the problem of socialism appears largely as a problem of size. The extreme socialists desire to run every nation as a single business concern. I do not suppose that Henry Ford would find much difficulty in running Andorra or Luxembourg on a socialistic basis. He has already more men on his pay-roll than their population. It is conceivable that a syndicate of Fords, if we could find them, would make Belgium Ltd. or Denmark Inc. pay their way. But while nationalization of certain industries is an obvious possibility in the largest of states, I find it no easier to picture a completely socialized British Empire or United States than an elephant turning somersaults or a hippopotamus jumping a hedge.
J. B. S. Haldane
People have many myths about anger that cause them to categorize the issue in a certain way. For instance, some people consider anger to be biological or hereditary, but this myth does not have any solid foundation. Although some people are more prone to anger due to their psychophysical make-up or emersion in the modes of passion and ignorance, their socialization or quality of association will have a greater impact on their reactions. Although we do bring forth other infl uences into a situation such as our karma, which affects the ways in which we respond to specifi c situations, it is a myth that anger is biological and a permanent, unchangeable aspect of the body.
Bhakti Tirtha Swami
Let true Christians then, with becoming earnestness, strive in all things to recommend their profession, and to put to silence the vain scoffs of ignorant objectors. Let them boldly assert the cause of Christ in an age when so many, who bear the name of Christians, are ashamed of Him: and let them consider as devolved on Them the important duty of suspending for a while the fall of their country, and, perhaps, of performing a still more extensive service to society at large; not by busy interference in politics, in which it cannot but be confessed there is much uncertainty; but rather by that sure and radical benefit of restoring the influence of Religion, and of raising the standard of morality.
William Wilberforce