Hello prof , in so many resources the integer part function E(x) is defined as a piecewise function such that which is the floor of x when x is greater than or equal to 0 and the ceiling of x when x is less than 0 , which means for x= -5.1 we have E(x) = -5 , is this a problem with how the function is defined in Algeria as if it's just the floor of x for all x in R and how different resources define it or it always has the same definition and i'm getting something wrong.
If the sequence is non increasing the limit is inf. If the sequence is non decreasing the limit is sup. Anyway this technique needs more details. You can use it with care.
![Solve in R : [5x]=4[x]](/img/1.gif)
Nice expelenation
Thank you, my pleasure.
Hello prof , in so many resources the integer part function E(x) is defined as a piecewise function such that which is the floor of x when x is greater than or equal to 0 and the ceiling of x when x is less than 0 , which means for x= -5.1 we have E(x) = -5 , is this a problem with how the function is defined in Algeria as if it's just the floor of x for all x in R and how different resources define it or it always has the same definition and i'm getting something wrong.
As far as I know we have two functions with respect to this item.
Integer part: floor and ceiling for all x of R.
Regards
شكرا استاذ جزاك الله خيرا
بارك الله فيكم. من دواعي سروري.
@@maamarbenbachir استاذ منفضلك هل لديك سلاسل تمارين محلولة للجبر1 والتحليل 1 بلغة انجليزية ؟
teacher please do the other ways to prove that [x+p] = [x] +p
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السلام عليكم ورحمة الله وبركاته ،سؤال من فضلك استاذ:
If the séquence convergence for L :lim un=L
«=»??
lim[un]=[L]
من فضلك
If the sequence is non increasing the limit is inf.
If the sequence is non decreasing the limit is sup. Anyway this technique needs more details. You can use it with care.
@@maamarbenbachir ربي يحفظك استاذ ،غدا باءذن الله نحاول نبرهن ونفصل اذا كانت اكثر من حالة