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Are rational numbers natural numbers'?

They can be but in general any number that can be expressed as a fraction is a rational number


How do you take the antiderivative of 1 over x?

The general formula for powers doesn't work in this case, because there will be a zero in the denominator. The antiderivative of 1/x is ln(x), that is, the natural logarithm of x.


Importance of statistics in mathematics?

Statistical plays a central role in almost all natural and social sciences. The methods of natural sciences are most reliable but conclusions draw from them are only probable, because they are based on incomplete evidence. Statistical helps in describing these measurements more precisely. Statistics is branch of applied mathematics. The large number of statistical methods like probability averages, dispersions, estimation etc… is used in mathematics and different techniques of pure mathematics like integration, differentiation and algebra are used in statistics.


Is a real number a natural?

Yes a real number is a natural since real is natural so anything real is natural and so a real number is natural.


True or false induction it a kind of thinking of thinking you use to form general ideas and rules based on mathrmatical formulas?

False. Induction is a method of reasoning used to form general conclusions based on specific observations or examples, not just mathematical formulas. In mathematics, mathematical induction is a specific technique used to prove statements about natural numbers, but the broader concept of induction applies to forming general ideas from empirical evidence across various fields.