Let z denote the set of all integers with addition defined in the usual way, and define scalar multiplication, denoted o, by:
alpha o k = [[alpha]].k for all k in z

where [[alpha]] denotes the greatest integer less than or equal to alpha, for example,
2.25 o 4 = [[2.25]].4 =2..4 = 8
show that z, together with these operations, is not a vector space. which axioms fail to hold?

City l has a temperature of −3 °f. city m has a temperature of −7 °f. use the number line shown to answer the questions: number line from negative 8 to positive 8 in increments of 1 is shown. part a: write an inequality to compare the temperatures of the two cities. (3 points) part b: explain what the inequality means in relation to the positions of these numbers on the number line. (4 points) part c: use the number line to explain which city is warmer. (3 points)