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# Number Sense

The topic number sense of 10th grade contains following sub topics and in each topic they are divided into individual subtopics which are explained clearly below by our math problem solver.

## Topics Covered under Number Sense Help

• Real Numbers
• Mathematical Induction
• Sets
• Sequence and Series
• Linear Inequalities

## Real Numbers

In Number Sense Help, real number may be either rational number or irrational; either algebraic and either positive, negative, or zero. Real numbers are used to measure continuous quantities. They may in theory be expressed by decimal representations that have an infinite sequence of digits to the right of the decimal point.Decimal number is a number which always uses 10 as its base and it is most widely used to solve the complex problems. It is denoted with a dot (.) in between it.

## Mathematical Induction

Mathematical induction is a method of mathematical proof typically used to establish a given statement is true of all natural numbers. It is done by proving that the first statement in the infinite sequence of statements is true, and then proving that if any one statement in the infinite sequence of statements is true,repeated for others.The method can be extended to prove statements about more general well-founded structures, such as trees; is known as structural induction, is used in mathematical logic and computer science. Mathematical induction in this extended sense is closely related to recursion.

## Sets

Set is a collection of distinct objects in the given objects.Suppose their are to set A and B and if every member of set A is also a member of set B, then A is said to be a subset of B, written A ? B.Set of all sub set is called power set.They are many fundamental operations which can be performed on sets and can be denoted with different symbols in sets.The realation between two sets can be identified by Vendiagram.

Relation is any subset of a Cartesian product.If a subset of AXB, called a "binary relation from A to B," is a collection of ordered pairs from (a,b) with first components from A and second components from B,they are related to ecah other.Subset of A×A is called a "relation on A."

## Sequence and Series

Sequence is a set of things that are in order.If the sequence goes on to infinite number it is called an infinite sequence,otherwise it is a finite sequence.They are different sequences like arthemetic,geometric,Triangular sequnces these are special sequnces which are discussed detail.Series representation of sequence depends on the difference between two digits and the difference should be sam ethrought of sequence then we can represent with mathematical induction formulas and simplify the equation.

## Linear Inequalities from 10th Grade Number Sense Help

Linear equation is an algebraic equation in which each term is either a constant or the product of a constant and with a single variable. It contains one or more variables.It occur with great regularity in applied mathematics.Slope can be identified ,Non-linear equations May be reduced to linear equations.When dealing with three or four variables, it is common to replace x1 with just x, x2 with y, and x3 with z, as appropriate.Inequalities that's left hand side will be not equal to right hand side.