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Hint: Instead of thinking a positive number one should also look for negative numbers too as negative integers do exist and are less than positive ones.

Complete step-by-step answer:

In the question we are asked to find out the smallest integer that can be written with two digits.

Before finding it we will first explain what is integer.

An integer (from the Latin integer meaning “whole”) is a number that can be written without a fractional component. For example 21, 4, 0, -2408 are integers while $975,5\dfrac{1}{2},\sqrt{2}$ are not.

The integer set consists of zero (0), the positive natural numbers (1, 2, 3….), also called whole numbers or counting numbers, and their additive inverses (that is, the negative integers -1, -2, -3…).

The set of integers is often denoted by a Z standing for Zahlen (numbers).

Z is a subset of the set of all rational numbers Q, in turn a subset of real number R. Like the natural numbers, rational and numbers are countably infinite.

Now as we know negative numbers are always less than positive numbers so we will choose two digit numbers from the set of negative numbers.

Hence the least two digits integer is -99.

Note: Students generally confuse themselves and they will write 10 which is not the correct answer as they forget about the negative numbers are also integers. That is why, while choosing the smallest integer they should take care of negative ones too so that the answer doesn’t get wrong.

Complete step-by-step answer:

In the question we are asked to find out the smallest integer that can be written with two digits.

Before finding it we will first explain what is integer.

An integer (from the Latin integer meaning “whole”) is a number that can be written without a fractional component. For example 21, 4, 0, -2408 are integers while $975,5\dfrac{1}{2},\sqrt{2}$ are not.

The integer set consists of zero (0), the positive natural numbers (1, 2, 3….), also called whole numbers or counting numbers, and their additive inverses (that is, the negative integers -1, -2, -3…).

The set of integers is often denoted by a Z standing for Zahlen (numbers).

Z is a subset of the set of all rational numbers Q, in turn a subset of real number R. Like the natural numbers, rational and numbers are countably infinite.

Now as we know negative numbers are always less than positive numbers so we will choose two digit numbers from the set of negative numbers.

Hence the least two digits integer is -99.

Note: Students generally confuse themselves and they will write 10 which is not the correct answer as they forget about the negative numbers are also integers. That is why, while choosing the smallest integer they should take care of negative ones too so that the answer doesn’t get wrong.

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