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The solution = is in fact a valid solution to the original equation; but the other solution, =, has disappeared. The problem is that we divided both sides by x {\displaystyle x} , which involves the indeterminate operation of dividing by zero when x = 0. {\displaystyle x=0.}
In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign. When seeking a solution, one or more variables are designated as unknowns. A solution is an assignment of ...
6 [6] Clay Mathematics Institute: 2000 Simon problems: 15 <12 [7] [8] Barry Simon: 2000 Unsolved Problems on Mathematics for the 21st Century [9] 22-Jair Minoro Abe, Shotaro Tanaka: 2001 DARPA's math challenges [10] [11] 23-DARPA: 2007 Erdős's problems [12] >927: 615: Paul Erdős: Over six decades of Erdős' career, from the 1930s to 1990s
Many easily stated number problems have solutions that require sophisticated methods, often from across mathematics. A prominent example is Fermat's Last Theorem . This conjecture was stated in 1637 by Pierre de Fermat, but it was proved only in 1994 by Andrew Wiles , who used tools including scheme theory from algebraic geometry , category ...
However, in Higgs' view, Brout and Englert did not explicitly mention the boson since its existence is plainly obvious in their work, [68]: 6 while according to Guralnik the GHK paper was a complete analysis of the entire symmetry breaking mechanism whose mathematical rigour is absent from the other two papers, and a massive particle may exist ...
Cardano's formula, the solution to general cubic equations. Cardano stated that it was discovered by Scipione del Ferro, who passed the knowledge to his student Antonio Maria Fior. Around 1535 Niccolò Fontana Tartaglia learned of this from Fior and re-derived the formula for the cubic, which he later shared with Cardano. [14] [15]
Melinda French Gates [2] (born Melinda Ann French; August 15, 1964) is an American philanthropist and a former multimedia product developer and manager at Microsoft.Born and raised in Dallas, Texas, she graduated from Duke University and started working at Microsoft in 1987.
Artificial intelligence (AI), in its broadest sense, is intelligence exhibited by machines, particularly computer systems.It is a field of research in computer science that develops and studies methods and software that enable machines to perceive their environment and use learning and intelligence to take actions that maximize their chances of achieving defined goals. [1]