I am learning interval notation. One of my friends said that besides from '('and '[',there is '{'. Is it true? Is there any " { or }"in interval notation? If yes, what is it used for?
Thank you so much :-)
Yes, you can use {} to describe an interval, but it is not part of the interval notation.
The use of {} is used to define a set which gives the same members as the interval notation, for example:
(4,7)=]4,7[={x|4<x<7}
The right hand side of the equal sign defines a set where the members are real numbers between 4 and 7, excluding 4 and 7.
I don't get your example and the use of { }, can you explain further?
Thank You =]
(4,7) is the normal interval notation indication all real numbers between 4 and 7 but excluding 4 and 7.
It can also be written as ]4,7[.
[4,7] is the interval notation also for including all real numbers between 4 and 7 but including the two limits, namely 4 and 7.
{x|4<x<7} is a set notation to define a set of real numbers between 4 and 7 and excluding 4 and 7. Another example of the set notation is
{4,5,6,7} for the set of four integers from 4 to 7.
In short, you can also define an interval using the set notation, but it is ot part of the intervl notation.2
OK. Thanks. =]
In interval notation, the symbols "(" and "[" are used to represent open and closed endpoints, respectively. The symbol "{" is not typically used in interval notation.
However, the symbol "{" is used in set notation to represent a set. In set notation, an interval can be expressed as a set of numbers enclosed within curly braces "{ }". For example, the interval (-∞,3) in interval notation would be expressed as {x | x < 3} in set notation.
It's important to note the distinction between interval notation and set notation, as they have different purposes and uses. Interval notation is primarily used to represent intervals on the number line, while set notation is used to represent collections or sets of numbers.