Find a fraction which, multiplied by itself, shall give 6, or... find the square root of 6. This can be shown to be an impossible problem; for it can be shown that no fraction whatsoever multiplied by itself, can give a whole number, unless it be itself a whole number disguised in a fractional form, such as 4⁄2 or 21⁄3. To this problem, then, there is but one answer, that it is self-contradictory. But if we propose the following problem,-to find a fraction which, multiplied by itself, shall give a product lying between 6 and 6 + a; we find that this problem admits of solution in every case. It therefore admits of solution however small a may be... as small as you please.
Augustus De MorganRelated topics
answer case find following form fraction fractional impossible lying multiply number problem product propose root show small solution squareRelated quotes
Ben, the ethics of sex is a thorny problem. Each of us is forced to grope for a solution he can live with - in the face of a preposterous, unworkable, and evil code of so-called "morals." Most of us know the code is wrong; almost everybody breaks it. But we pay Danegeld by feeling guilty and giving lip service. Willy-nilly, the code rides us, dead and stinking, an albatross around the neck.
You, too, Ben. You fancy yourself a free soul - and break that evil code. But faced with a problem in sexual ethics new to you, you tested it against that same Judeo-Christian code... so automatically your stomach did flip-flops... and you think that proves you're right and they're wrong. Faugh! I'd as lief use trial by ordeal.
Robert A. Heinlein
You probably know that this week Britain has been terrorized by an underclass of welfare-dependent, drug-addled criminal scum who have been allowed to run riot in the streets because the police haven't been allowed to do their job and protect the public. The media is full of speculation about why it happened and what is the root cause. Well, that's easy. The root cause is stupidity. A complete lack of imagination. A stunted, feral view of the world that amounts to self-inflicted moral and mental disablement. And it's the direct product of an entitlement culture that rewards idleness, encourages victimhood, and compensates criminals.
Pat Condell
We must account for that inheritance. And we, especially those of us who enjoy the privilege that comes with being the majority, must confront the biases that are inescapable parts of the human condition. We must speak the truth about our shortcomings as law enforcement, and fight to be better. But as a country, we must also speak the truth to ourselves. Law enforcement is not the root cause of problems in our hardest hit neighborhoods. Police officers, people of enormous courage and integrity, in the main, are in those neighborhoods, risking their lives, to protect folks from offenders who are the product of problems that will not be solved by body cameras.
James Comey
Shall we not perhaps be told, on the other hand, that if the sinner suffers an eternal punishment, it is because he does not cease to sin? - for the damned sin without ceasing. This however is no solution to the problem, which derives all its absurdity from the fact that punishment has been conceived as vindictiveness or vengeance, not as correction, and has been conceived after the fashion of barbarous peoples. And in the same way hell has been conceived as a sort of police institution, necessary in order to put fear into the world. And the worst of it is that it no longer intimidates, and therefore will have to be shut up.
Miguel de Unamuno
I am primarily painting from photographs these days (from illustrated magazines but also from family photos), in a sense this is a stylistic problem, the form is naturalistic, even though the photograph is not nature at all but a prefabricated product (the "second-hand world” in which we live), I do not have to intervene artistically with style, since the stylization (deformation in form and color) contributes only under very particular circumstances toward clarifying and intensifying an object or a subject (generally stylization becomes the central problem which obscures everything else (object, subject), it leads to an unmotivated artificiality, an untouchable formalist taboo.
Gerhard Richter
