Math Question

[Wow Strong Armz]

i have no idea what to search or where to look but i wanted to know what is the diffrence between say (0,infinity] and [0,infinity]. The brackets is what im looking for

 

[Knickerbocker]

Parenthesis mean "non-inclusive" and brackets mean "inclusive"

For example, [0,5) includes all values greater than or equal to zero and less than 5.

If it were [0,5], it would be all values greater than or equal to zero and less than or equal to 5.

By the way, I think that + or - infinity is always considered non-inclusive, so it will always have the parenthesis.

 

[Wow Strong Armz]

thanks, so for this problem what is the range of the function f(x) = e^(-x) why would the answer be (0,infinity] and not [0,inifinity] as when i be 0 in the calc i get 1 so that would have to be part of the range thanks

 

[Knickerbocker]

thanks, so for this problem what is the range of the function f(x) = e^(-x) why would the answer be (0,infinity] and not [0,inifinity] as when i be 0 in the calc i get 1 so that would have to be part of the range thanks

When you are looking at values for x, you are observing the domain. The range is the values for f(x).

e^-99999 is a very small number very close to 0
e^-99999999 is an even smaller number even closer to 0

For that function, the limit as -x approaches -infinity is 0. So zero is non-inclusive. e^infinity is defined to be infinity, so it is inclusive for that.

 

[snvplayer]

e^(-x) = 1 / (e^x)

1 / 9999999999 is pretty much equal to 0.

 

[Knickerbocker]

e^(-x) = 1 / (e^x)

1 / 9999999999 is pretty much equal to 0.

It's close to zero, but it's not equal to zero. F(x) approaches zero as x approaches infinity; zero is the limit. So it is open parenthesis and not the open bracket as zero is non-inclusive.