Do all the numbers belong to same slot in the Hashtable? I was reading the CLRS. In the Hashing Chapter on page 262 a statement says: "For example, if we know that the
keys are random real numbers $k$ independently and uniformly distributed in the range $0 \leq k &lt; 1$, then the hash function $h(k)= \lfloor km \rfloor$."

Question: Does Uniformly distributed meant all numbers have equal probability.
if so then all numbers have the same $k$ values and belong to the same slot.
Keys are uniformly distributed means that they are drawn from a space with equal probability.

So if we set the hash function to be $h(k)=\lfloor{km}\rfloor$, then each given element is equally likely to hash into any of the $m$ slots. (Refer to the definition of simple uniform hashing in page 259 CLRS)

Yes, it is true that each element with key $k$ will be hashed to the same slot. But the point is the elements are chosen uniformly independently, so they have the same probability to hash to any of the $m$ slots.