Virtually
In mathematics, especially in the area of abstract algebra which studies infinite groups, the adverb virtually is used to modify a property so that it need only hold for a subgroup of finite index. Given a property P, the group G is said to be virtually P if there is a finite index subgroup H≤G such that H has property P.
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Famous quotes containing the word virtually:
“Let those talk of poverty and hard times who will in the towns and cities; cannot the emigrant who can pay his fare to New York or Boston pay five dollars more to get here ... and be as rich as he pleases, where land virtually costs nothing, and houses only the labor of building, and he may begin life as Adam did? If he will still remember the distinction of poor and rich, let him bespeak him a narrower house forthwith.”
—Henry David Thoreau (1817–1862)
“It may be tempting to focus on the fact that, even among those who support equality, men’s involvement as fathers remains a far distance from what most women want and most children need. Yet it is also important to acknowledge how far and how fast many men have moved towards a pattern that not long ago virtually all men considered anathema.”
—Katherine Gerson (20th century)
“Any historian of the literature of the modern age will take virtually for granted the adversary intention, the actually subversive intention, that characterizes modern writing—he will perceive its clear purpose of detaching the reader from the habits of thought and feeling that the larger culture imposes, of giving him a ground and a vantage point from which to judge and condemn, and perhaps revise, the culture that produces him.”
—Lionel Trilling (1905–1975)