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The hydra effect or hydra paradox owes its name to the Greek legend of the Lernaean Hydra which grew two heads for each one cut off, and is used figuratively for counter-intuitive effects of actions to reduce a problem which result in stimulating its multiplication. Most notably, scientists have proposed that ecological systems can exhibit a ...
Multiplication by a positive number preserves the order: For a > 0, if b > c, then ab > ac. Multiplication by a negative number reverses the order: For a < 0, if b > c, then ab < ac. The complex numbers do not have an ordering that is compatible with both addition and multiplication. [30]
addition and multiplication of random variables are both commutative; and; there is a notion of conjugation of random variables, satisfying (XY) * = Y * X * and X ** = X for all random variables X,Y and coinciding with complex conjugation if X is a constant. This means that random variables form complex commutative *-algebras.
Karatsuba multiplication of az+b and cz+d (boxed), and 1234 and 567 with z=100. Magenta arrows denote multiplication, amber denotes addition, silver denotes subtraction and cyan denotes left shift. (A), (B) and (C) show recursion with z=10 to obtain intermediate values. The Karatsuba algorithm is a fast multiplication algorithm.
Division is the inverse of multiplication, meaning that multiplying and then dividing by the same non-zero quantity, or vice versa, leaves an original quantity unchanged; for example () / = (/) =. [12]
The power of 3 multiplying a is independent of the value of a; it depends only on the behavior of b. This allows one to predict that certain forms of numbers will always lead to a smaller number after a certain number of iterations: for example, 4 a + 1 becomes 3 a + 1 after two applications of f and 16 a + 3 becomes 9 a + 2 after four ...
In April 2007, a rumour was confirmed on the Swedish talk show Bert that The Pirate Bay had received financial support from right-wing entrepreneur Carl Lundström. This caused some consternation since Lundström, an heir to the Wasabröd fortune, is known for financing several far-right political parties and movements like Sverigedemokraterna and Bevara Sverige Svenskt (Keep Sweden Swedish).
Dividing integers in a computer program requires special care. Some programming languages treat integer division as in case 5 above, so the answer is an integer. Other languages, such as MATLAB and every computer algebra system return a rational number as the answer, as in case 3 above.
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