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Sponsored by the Center for Science and Technology Development of the Ministry of Education
Supervised by Ministry of Education of the People's Republic of China
We found a problem on real functional limits that can't be solved through all analytical tools that we known. Obviously, there is a crack in the basis of classical analysis, while the problem doesn't be solved. We mended the crack through improving the ending principle on functional limit attributed to Heine and defining a special function of one variable as a fake-function of two variables.
Keywords:limit of a function, Heine's ending principle, fake-function of two variables