- #1

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h(x) = 1/x and the function h has domain R excluding 0, could somebody please explain how the two open intervals include (- infinity, 0) and (0, infinity)?

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- #1

- 86

- 0

h(x) = 1/x and the function h has domain R excluding 0, could somebody please explain how the two open intervals include (- infinity, 0) and (0, infinity)?

(Headbang)

- #2

h(x) = 1/x and the function h has domain R excluding 0, could somebody please explain how the two open intervals include (- infinity, 0) and (0, infinity)?

(Headbang)

Hi Casio,

You already said the domain was all real numbers except 0. To represent that in interval notation you would use the union of the two intervals you have.

$$ (- \infty, 0) \cup (0, +\infty)$$

And this says the domain includes all real numbers less than 0 together with all real numbers greater than 0. Zero is excluded in the notation by using paretheses instead of brackets.

- #3

Gold Member

MHB

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Kind regards

$\chi$ $\sigma$

- #4

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Although they are included in the brackets, and I can see them there, they are not included, which is what confused me.

- #5

Science Advisor

Homework Helper

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[a, b] means "all numbers between a and b and a and b themselves".

In set notation: [tex][a, b]= \{ x| a\le x\le b\}[/tex]

(a, b) means "all numbers between a and b

In set notation: [tex](a, b)= \{ x| a< x< b\}[/tex]

[a, b) means "all numbers between a and b including a but

In set notation: [tex][a, b]= \{ x| a\le x< b\}[/tex]

(a, b] means "all numbers between a and b including b but

In set notation: [tex][a, b]= \{ x| a< x\le b\}[/tex]

- #6

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[a, b] means "all numbers between a and b and a and b themselves".

In set notation: [tex][a, b]= \{ x| a\le x\le b\}[/tex]

(a, b) means "all numbers between a and bnotincluding a and b".

In set notation: [tex](a, b)= \{ x| a< x< b\}[/tex]

[a, b) means "all numbers between a and b including a butnotb".

In set notation: [tex][a, b]= \{ x| a\le x< b\}[/tex]

(a, b] means "all numbers between a and b including b butnota".

In set notation: [tex][a, b]= \{ x| a< x\le b\}[/tex]

Very much appreciated for the help and effort you have put into this thread. May I expand and ask additonal questions in relation to what you have wrote above please.

In your first line of set notation, this I read to mean that the interval is closed.

In your second line of set notation, this I read to mean the interval is open.

In your third line of set notation, this I read to mean the interval is half open or half closed.

In your forth line of set notation, this I read to mean the interval is also open or half closed.

The round bracket being open and the square bracket being closed.

If I am understanding the above correctly, the inequalities when used with real numbers would be used as the domain, and if by example I said;

-1

The problem I can't understand at the present is in the use of infinity, whether that be positive or negative infinity and how to correctly interpret it in the use of solutions to questions?

- #7

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One always use [tex](-\infty,0][/tex] and [tex](0.\infty)[/tex] i.e. with infinity we use ( or ).The problem I can't understand at the present is in the use of infinity, whether that be positive or negative infinity and how to correctly interpret it in the use of solutions to questions?

[tex](-\infty,0][/tex] is the set of all real numbers less than

[tex](0,\infty)[/tex] is the set of all real numbers

Notice how in the first case ] is inclusive and in the second ( is exclusive.

- #8

Science Advisor

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