Proof of buffers inability to maintain exact same pH I was wondering if the following is a legitimate proof of the statement above. Assume we have 

HA -> A- + H+

where [HA] + [A-] is our buffer. 

If we add a small amount of H+ one of two things will happen:

1) The H+ will not react with A- ...thereby raising the pH so we are done.

2) The H+ will react with A- ...converting to [HA]

looking at the HH equation we know that 

pH = pKa + log(ratio)

since ratio_before != ratio_after 

pH_after = pKa + log(ratio_after) and pH_before = pKa + log(ratio_before) 

so therefore 

pH_after - log(ratio_after) = pH_before -log(ratio_before) 

Now assume pH_after == pH_before.... we get -log(ratio_after) = -log(ratio_before) which is a contradiction of above, so pH_after != pH_before.

What are your thoughts?
A buffer is a solution that can resist pH change upon the addition of
  an acidic or basic components. It is able to neutralize small amounts
  of added acid or base, thus maintaining the pH of the solution
  relatively stable.


Buffers do not maintain exact same pH, but keep it relatively stable i.e. close to the original value.
log(ratio) &lt;&lt; pKa, therefore, pH changes will be minimal, unless substantial amount of acid has been added to the solution.

For instance, when the ratio between the conjugate base/acid is equal to 1, the pH = pKa. 

If the ratio between the two is 0.10, the pH drops by 1 unit from pKa since log (0.10) = -1. 

If a ratio increases to a value of 10, then the pH increases by 1 unit since log (10) = 1. 

As you can see, changing ratio by 10 times, affects pH value only by 1 unit.