Hi guys ; once again I think I'm not getting the idea of accumulating sub-quantities(sum of sub-quantities) to gain the required quantity; and what I mean by that is actually my question down.

Well, I will visualize an example which will convey my problem with accumulating(sum) ; lets assume there's a bus which arrived at 7:00 at the station and his last left over that station is 10:00 and then the bus stops working ; given that between 7:00 and 10:00 the bus has passed over that station four time at 7:00, 8:00, 9:00, 10:00 .

the question is, find the total time that the bus is worked? it's simple to say from 10:00 till 7:00 which 10-7=3 ; but I'm confusing is how can I get the same answer if I added: (8:00-7:00) + (9:00-8:00) + (10:00-9:00) =3 ; my problem is why the accumulating the time between the pieces then I will get the total time between 7:00---10:00 ; exactly what I'm confusing at and what I'm thinking to solve the problem is like this:

frmo 7:00 till 8:00 the bus was working then this amount I must add it to the sum .., afterwards from 8:00+(not 8:00) till 9:00 I need to add this sum .. here is my problem I need to say in the second summation "8:00+" and not "8:00" .. so how why we are adding from 8:00 till 9:00 and not (8:00+) till 9:00 ?

actually why it doesn't matter to say 8:00 or 8:00+ is the same thing ?! isn't the amount(time) at concrete point "8:00" is smaller than the amount of time at concrete point "8:00+"?

To sum up; what I think and find it hard that I'm convinced that at boundaries - "between" - will have also a quantity so I need to say boundary+ or boundary- in accumulation .

thanks for helpers and sorry for that confusion.

Well, I will visualize an example which will convey my problem with accumulating(sum) ; lets assume there's a bus which arrived at 7:00 at the station and his last left over that station is 10:00 and then the bus stops working ; given that between 7:00 and 10:00 the bus has passed over that station four time at 7:00, 8:00, 9:00, 10:00 .

the question is, find the total time that the bus is worked? it's simple to say from 10:00 till 7:00 which 10-7=3 ; but I'm confusing is how can I get the same answer if I added: (8:00-7:00) + (9:00-8:00) + (10:00-9:00) =3 ; my problem is why the accumulating the time between the pieces then I will get the total time between 7:00---10:00 ; exactly what I'm confusing at and what I'm thinking to solve the problem is like this:

frmo 7:00 till 8:00 the bus was working then this amount I must add it to the sum .., afterwards from 8:00+(not 8:00) till 9:00 I need to add this sum .. here is my problem I need to say in the second summation "8:00+" and not "8:00" .. so how why we are adding from 8:00 till 9:00 and not (8:00+) till 9:00 ?

actually why it doesn't matter to say 8:00 or 8:00+ is the same thing ?! isn't the amount(time) at concrete point "8:00" is smaller than the amount of time at concrete point "8:00+"?

To sum up; what I think and find it hard that I'm convinced that at boundaries - "between" - will have also a quantity so I need to say boundary+ or boundary- in accumulation .

thanks for helpers and sorry for that confusion.

Last edited: