Research on Property of Infinitesimal Functions

Objective To research the property of the finite power,the sum of infinitude countable,the product of infinitude countable,the extract of the infinity and the power of the infinity of infinitesimal about the infinitesimal functions(sequence).Methods It gives the precise definitions of the finite power,the sum of infinitude countable,the product of infinitude countable,the extract of the infinity and the power of the infinity of infinitesimal about the infinitesimal functions(sequence).The results is obtained with definition and some examples.Results The finite power of infinitesimal is infinitesimal,the others are unfixed,and moreover,they are also infinitesimal on the appropriate condition.At last,it proves that the sufficient condition about the product of infinitude of infinitesimal is also infinitesimal.Conclusion The finite sum,product and power of the infinitesimal functions(sequence) are infinitesimal.However,the sum of infinitude countable,the product of infinitude countable,the extract of the infinity and the power of the infinity of the infinitesimal functions(sequence) are unfixed.And it is important to understand the definition.