Difference between "to remember" vs "for remembering"

It seems that I have found the answer here. Considering the aforementioned page from cambridge.org, I understand this way:

The usage of for + ing may be right when we want to express:

1. Function of something, for example:

   • We need something for storing recyclable materials.
   • Eclipse is one of the most popular tools for developing software applications.

2. Reason of something, for example::

   • You should talk to Jane about it. You know, she’s famous for being a good listener.

3. But NOTOurPurpose/intention, for example:

   • I am going to university for visiting [to visit] my professor.
   • There is a lot of juice for drinking [to drink].

My Conclusion:

It appears to me that the subject is important here. That means if I want to express my own intention or if we want to express our own purpose from doing something, then we fall into the last (third) scenario (were for + ing should not be used)

On the other hand, when we are speaking exclusively about some other people/things (nigher me, nor we are involved), then we may describe the function or reason as well as [even] the purpose/intention for usage/existence of something else with the for + ing construct.

for = for the purpose of

to = in order to

remembering = the ongoing or continuing process [that is uncompleted at the time referred to] of bringing [something] to mind .

remember = one instance of the action of bringing [something] to mind.