A real number x is recursively approximable if it is a limit of a computabl
e sequence of rational numbers. If, moreover. the sequence is increasing (d
ecreasing or simply monotonic), then x is called left computable (right com
putable or semi computable). x is called weakly computable if it is a diffe
rence of two left computable real numbers. We show that a real number is we
akly computable if and only if there isa computable sequence (x(s))(s is an
element ofN) of rational numbers which converges to x weakly effectively,
namely the sum of jumps of the sequence is bounded. It is also shown that t
he class of weakly computable real numbers extends properly the class of se
mi-computable real numbers and the class of recursively approximable real n
umbers extends properly the class of weakly computable real numbers. (C) 20
00 Academic Press.