Just as negative and fractional rational numbers are formed by a new creation, and as the laws of operating with these numbers must and can be reduced to the laws of operating with positive integers, so we must endeavor completely to define irrational numbers by means of the rational numbers alone. The question only remains how to do this.
Richard DedekindRelated topics
creation define endeavor fractional irrational negative numbers positive question rational remains means laws integersRelated quotes
One of the first algebraists to accept negative numbers was... placed negative numbers on a par with positive numbers and gave both roots of a quadratic equation, even when both were negative. Both Girard and Harriot used the minus sign for the operation of subtraction and for negative numbers.
Morris Kline
Though Wallis was advanced for his times and accepted negative numbers, he thought they were larger than infinity but not less than zero. In his Arithmetica Infinitorum (1655), he argued that since the ratio a/0, when a is positive, is infinite, then, when the denominator is changed to a negative number, as in a/b with b negative, the ratio must be greater than infinity.
Morris Kline
Dadaism has launched an attack on the fine arts. It has declared art to be a magic opening of the bowels, administered an enema to the Venus of Milo, and finally enabled 'Laocoon and Sons' to ease themselves after a thousand-year struggle with the rattlesnake. Dadaism has reduced positive and negative to utter nonsense. It has been destructive in order to achieve indifference.
Jean Arp
Society today is no longer in revolt against particular laws which it finds alien, unjust, and imposed, but against law as such, against the principle of law. And yet we must not regard this revolt as entirely negative. The energy that rejects many obsolete laws is an entirely positive impulse for renewal of life and law.
Abraham Joshua Heschel
The job numbers are positive. We've had more jobs created now than were lost during the recession. We're seeing that the creation, we're seeing those numbers not only grow but shift toward the private sector and shift toward full-time employment and these are all signs that the recovery is taking some hold but we're not out of woods.
Stephen Harper
