The beahave of "infinity part"

shahar

Junior Member
Joined
Jul 19, 2018
Messages
154
Suppose I have a function that has:
"When x -> infinity, f(x) -> infinity"
(1)
How could I know the part of graph continue still going on with no stop point?
a)
You can say by trial and error for example.
But that not rigors reason.No?
b)
You can say by function investigation function you can "define" the of graph of infinity.
Why by little steps you can define it and not by huge number of step?
How do you know you have all the importation by ?
Why there is no loss of information by investigation so your know what about the continue part?
(2) Is the a site on the history of the development on the investigation of function?
continue part = the part to go infinity
 
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HallsofIvy

Elite Member
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Jan 27, 2012
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4,934
Frankly, I don't understand what you are asking. Perhaps it is a language problem. You say "Suppose I have a function that has: "When x -> infinity, f(x) -> infinity". Do you mean you are given that and then want to know what the graph looks like or are you asking how to determine whether that is true or not?
 

pka

Elite Member
Joined
Jan 29, 2005
Messages
8,099
Suppose I have a function that has:
"When x -> infinity, f(x) -> infinity"
(1) How could I know the part of graph continue still going on with no stop point? a)You can say by trial and error for example.
But that not rigors reason.No? continue part = the part to go infinity
If \(\displaystyle \mathop {\lim }\limits_{x \to \infty } f(x) = \infty \) then \(\displaystyle \left( {\forall n \in {\mathbb{Z}^ + }} \right)\left( {\exists x>n} \right)\left[ {f(x) > n} \right]\)
This is a strange question: if \(\displaystyle f(x)\to\infty\) then the function get bigger & bigger.
 

shahar

Junior Member
Joined
Jul 19, 2018
Messages
154
If \(\displaystyle \mathop {\lim }\limits_{x \to \infty } f(x) = \infty \) then \(\displaystyle \left( {\forall n \in {\mathbb{Z}^ + }} \right)\left( {\exists x>n} \right)\left[ {f(x) > n} \right]\)
This is a strange question: if \(\displaystyle f(x)\to\infty\) then the function get bigger & bigger.
O.K.
So, I will describe what I understood.
(1) How can I know what will happen in the part infinity?
-First I need to investigate it and it help to know if there is no function in infinity (the domain is not defined there).
The easy case to know what happen in infinity:
Extreme example with no domain: f = K (K = constant and f not a function)
f = x/0 etc.
And Now What I miss:
The x-value of the coordinate is growing by one unit that is one when draw the x-y coordinate.
So if the operation is get bigger I will know that the function go to infinity and it defined it by investigate.
So, I will ask what the reason to know if operations are "getting" to infinity. I have two tools:
-graph function (Calculus)
-Induction if the "function" input if Natural number (Number Theory)
 

pka

Elite Member
Joined
Jan 29, 2005
Messages
8,099
O.K.
So, I will describe what I understood.
(1) How can I know what will happen in the part infinity?
-First I need to investigate it and it help to know if there is no function in infinity (the domain is not defined there).
The easy case to know what happen in infinity:
Extreme example with no domain: f = K (K = constant and f not a function)
f = x/0 etc.
And Now What I miss:
The x-value of the coordinate is growing by one unit that is one when draw the x-y coordinate.
So if the operation is get bigger I will know that the function go to infinity and it defined it by investigate.
So, I will ask what the reason to know if operations are "getting" to infinity. I have two tools:
-graph function (Calculus)
-Induction if the "function" input if Natural number (Number Theory)
This is an honest if brutal answer which is no way meant to belittle you.
You simply do not have a sufficient mathematical background to even begin to understand the answer t this question.
To get sufficient background you need to do a course in preCalculus and a course in Calculus.
There are no shortcuts. You just need to spend to time to do the necessary work to prepare yourself to understand the replies.
 
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