Do Bases and Acids actually react with each other? Let's say we have $5$ $\ce{HCl}$ molecules and we dump them into a container full of water. It's a strong acid so all $5$ $\ce{H+}$ ions would react with water and create $\ce{H3O+}$. It reacts with the water, right?

Now, we add $5$ $\ce{NaOH}$ molecules down there. They all react with some water molecules of their own as well and create $5$ $\ce{OH-}$. So now we have $5$ $\ce{H3O+}$ and $5$ $\ce{OH-}$. Those two don't react with each other, correct? They just react with the water molecules and balance each other out, giving us a neutral solution. 

I am unsure of this. Is this true? Thanks in advance.
$$\ce{NaOH + HCl -&gt; NaCl + H2O}$$

$$\ce{Na+ + Cl- + OH- + H+ -&gt; Na+ + Cl- + H2O_{(l)}}$$
Both sides $\ce{Na+}$ ans $\ce{Cl-}$ cancel out remaining reaction

$$\ce{H+ + OH- &lt;=&gt; H2O_{(l)}}$$

Any strong acid and strong base reaction the remaining reaction is hydrolization of water.