A property tester with high probability accepts inputs satisfying a given property and rejects
inputs that are far from satisfying it. A tolerant property tester, as defined by Parnas, Ron
and Rubinfeld, must also accept inputs that are close enough to satisfying the property. We
construct properties of binary functions for which there exists a test making a constant number
of queries, but yet there exists no such tolerant test. The first construction uses Hadamard codes
and long codes. Then, using Probabilistically Checkable Proofs of Proximity as constructed by
Ben-Sasson et. al. we exhibit a property which has constant query intolerant testers but for
which any tolerant tester requires n^c queries for some c>0.