Quadratic Probing Infinite Loop? I understand the definition of Load Factor and how Quadratic Probing works. But what happens in the case where quadratic probing cannot find an empty slot for a new element?

According to https://en.wikipedia.org/wiki/Quadratic_probing:


  In the case of quadratic probing, with the exception of the triangular
  number case for a power-of-two-sized hash table[2], there is no
  guarantee of finding an empty cell once the table gets more than half
  full, or even before the table gets half full if the table size is not
  prime.


Does this mean that Load Factor should always be 0.5 for a Hash Table that uses Quadratic Probing?

What is the proof of this claim?
No. It means you should count how many slots you have checked, and if you have checked more than the available number of slots, you resize the table. 

In practice, if you regularly visit more than ten slots, then either the hash function is bad (nothing you can do about it while your program is running), or your load factor is too large. Not finding an empty slot will only happen if an attacker can decide your hash values.