Prove that the set of integers is countable.
A set is countable if there exists a bijection between the set and the set of natural numbers \( \mathbb{N} \). The set of integers \( \mathbb{Z} \) is countable _________ ___ ________ _________ _________ __________ _________.
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दिखाइए कि अनुक्रम (an), एकदिष्ट है, जहाँ उत्तर की पुष्टि कीजिए। । क्या (an) कॉशी अनुक्रम है? अपने
Give an example of a series ∑ such that ∑
is not convergent but the
sequence converges to 0.
सातत्य की अनुक्रमिक परिभाषा द्वारा सिद्ध कीजिए कि
द्वारा परिभाषित फलन f असतत है, I
चरम मानों के लिए फलन f(x) = (x+1)3 (x-3)2 की जाँच कीजिए।
Are the following statements true or false? Give reasons for tour answers.
a) -2 is a limit point of the interval 1-3,2].
b) The series is divergent.
The function, f(x)=sin² x is uniformly continuous in the interval [0, π).
d) Every continuous function is differentiable.
e) The function f defined on R by
is irrational Is integrable in the interval [2,3].
For the function, defined over [1,5], verify:
where P is the partition which divides [1.5] into four equal intervals.
Using the principle of mathematical induction, prove that is natural numbuer.