thermodynamics - Confused why delta ∆Q and dQ don't make sense for heat Q - Chemistry Stack Exchange

In my chemistry teacher's notes, some notations concerning the heat $Q$ are marked as inappropriate. $Q$: yes d$Q$: no $\delta Q$: yes $\Delta Q$: no In the second bullet in the screenshot below

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Clausius Inequality says the integral of dq/T for a process is less than equal to zero. Also any process needs to have ∆s=dq/T >0. Isn't this contradictory? - Quora

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