A function is "differentiable" if it has a derivative. A function is "continuous" if it has no sudden jumps in it. Until today, I thought these were merely two equivalent definitions of the same concept. But I've read some stuff today which seems to be claiming that this is not the case. The obvious next question is "why?" Several answers were given, but I don't understand any of them. In particular, Wikipedia and one of the replies above both claim that |x| has no derivative. Can anyone explain this extremely unexpected result? Apparently some people dislike the fact that this is non-obvious to me. To be clear: I am not saying that the result is untrue. (I'm sure many great mathematicians have analysed the question very carefuly and are quite sure of the answer.) I am saying that it is extremely perplexing. (As a general rule, mathematics has a habit of doing that.

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Religion goes hand in hand with fatuity, while science keeps abreast with civilization. Science is the activity and knowledge to understand, explore, and interpret the laws of nature, human society, and thinking. Civilization is a voluntary behavior of man formed on the basis of the correct understanding of material world and nonmaterial world. Without the development and progress of science, civilization is only an extravagant hope. The symbol for real civilization is: no slightest conflict between man and man, man and society, and man and nature, and the sustained harmony without the regulations of laws and without the mechanisms of supervision. Scientists are people who have discovered and can clearly describe or explain a certain law in the field of nature, society, and thinking, which is universally valid within a given limit of time and space. Science and scientist are offspring of the Greatest Creator. The Greatest Creator has not created religion, but he has created science and scientist. A real scientist cannot deny the existence of the Greatest Creator, because all that are created by the Greatest Creator are not a result of random actions but are based on science, laws, and principles. The road of science is the road of the Greatest Creator. Scientists are nearest to the Greatest Creator.

Religion is a spiritual and psychological activity through which man gets to know, believe in, worship, and follow god and Buddha. Strictly speaking, only Christianity and Buddhism can be called real religions.Christianism is the religion of god, and Buddhism is the religion of Buddha. In the future Christianity and Buddhism will be the only religions remaining, and the rest will gradually perish with the development of science and the progress of mankind. Christianity and Buddhism are two relatively independent and complete religions as wellas two contradictory religions. However, as a social phenomenon, religion will ultimately perish with the passage of time and in the future the great variety of religions will be unified as one single religion. No matter whether it is created by man, god, or Buddha or how difficult it is for its followers to accept the reality, the religion will finally die out if it cannot answer all the questions raised by man and cannot explain all the phenomena of the nature and life of the universe, because this religion can no longer guide man.

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The Samsung Galaxy S' successor has indeed been topic to much attention and it has by certain been said to function as the smartphone of the year. I will take a nearer turn to see whether this claim is true or perhaps not.