The formula for calculating damage reduction from armor in League of Legends is
Damage Reduction = Total Armor / (100 + Total Armor)
It seems clear to me that this formula dictates that adding more armor has diminishing returns.
For example, let's say my champion has 50 armor, which gives damage reduction of 33.33% and I buy an item that gives 25 more armor; then my champion's total armor would be 75 and damage reduction would be 42.86%. That means I saw a 28.6% increase in damage reduction (damage reduction was increased by 9.53%). Now let's say I buy another of these items with 25 armor. Now my champion's armor will be at 100 which gives damage reduction of 50%. That means I saw a 16.66% increase in damage reduction (damage reduction was increased by 7.14%).
Therefore, from the first 25 armor item I bought got me 9.53% damage reduction, while the second time I bought the item it only got me 7.14% damage reduction. It looks to me like it was 25.08% less effective the second time I bought it. That screams diminishing returns to me. Why would someone say otherwise? Would they say anything different about Magic Resistance?
Note: This question was inspired by a comment thread which started off of this question: http://gaming.stackexchange.com/questions/5601/what-is-the-formula-for-armor-magic-resist-reduction/5602#5602. I have heard similar insinuations made before, though, implying that magic resist and armor are somehow different in the department of diminishing returns (although I am not sure if that was implied in the comments on the related question).