# Problems from The set of the natural numbers, order and representation

Which of these numbers are natural?

a) $2.3$

b) $80$

c) $2$

d) $-12$.

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### Development:

a) Can we say: "I have $2.3$ brothers?"" No, perhaps we have two brothers, perhaps three, but we can nothave $2.3$.

b) In this case you can say, for example: "In this field there are $80$ sheep." Therefore, it is a natural number.

c) As in the previous case, it can be used to count things, "My brother is two years old." That is to say, it is also a natural number.

d) This is not for counting objects: "Tomorrow $-12$ guests will visit us!" is not correct.

### Solution:

$2.3$ is not a natural number.

$80$ is a natural number.

$2$ is a natural number.

$-12$ is not a natural number.

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Write, using the symbols $<$ and $>$, the following sentences:

a) $5$ is greater than $3$

b) $2$ is less than $7$

c) $4$ is greater than $5$

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### Development:

a) $5$ is greater than $3$ is the same as $5 > 3$.

b) $2$ is less than $7$ is the same as $2 < 7$.

c) We can write $4 > 5$, but it's not true because $4$ isn't greater than $5$.

### Solution:

a) $5 > 3$

b) $2 < 7$

c) $4$ is greater than $5$ can be translated to $4 > 5$, which is false.

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