一个与自然数有关的命题，若n=k（k∈N）时命题成立可以推出n=k+1时命题也成立．现已知n=10时该命题不成立，那么下列结论正确的是：______（填上所有正确命题的序号）
①n=11时该命题一定不成立；
②n=11时该命题一定成立；
③n=1时该命题一定不成立；
④至少存在一个自然数n0，使n=n0时该命题成立；
⑤该命题可能对所有自然数都不成立．
由题意可知，原命题成立则逆否命题成立，
P（n）对n=10时该命题不成立，（否则n=11也成立）．
同理可推得P（n）对n=2，n=1也不成立．所以③正确，⑤正确
故答案为：③⑤．
| Every summer, Jean Piaget retreats to his cabin in the Alps, where he spends most of his days analyzing the mass of research data generated over the past year at his Center for Genetic Epistemology. During long walks along the mountain trails, he mulls over the latest experimental results, and in the cool mountain evenings, he formulates his conclusions. With the approach of fall, he will descend from the mountain, manuscript for a book and several journal articles in hand. This time-honored procedure of careful observation followed by seclusion for thought and synthesis, has enabled him to become the most prolific, if not the most famous psychologist of the century. Piaget has only been widely known in this country since the 1960s, when his works were translated from their original French. But he has been recognized as an expert in the field of cognitive development in Europe since the 1930s. In fact, Piaget’s publishing career can be traced to the year 1906, when as a child of ten, he published his careful notes on the habits of an albino sparrow he observed near his home in Switzerland. After his precocious debut as an ornithologist, he took an after school job at the local natural history museum, soon becoming an expert on mollusks. At the age of sixteen he was recommended for a curator’s position at the natural history museum in Geneva, but declined in favor of continuing his education. He studied natural science at the University of Neuchatel, obtaining his doctorate at the age of twenty-one. His readings in philosophy stimulated an intense interest in epistemology-the study of humans acquire knowledge. Convinced that cognitive development had a genetic basis. Piaget decided that the best way to approach epistemology would be through its behavioral and biological components. Psychology appeared to be the discipline that best incorporated this approach. |
Piaget can be best regarded as a psychologist who
A．emphasizes the mental processes.
B．stresses the importance of the biological basis.
C．places more emphasis on the behavioral components.
D．sees observations as being more important than others.
