You can't add different things together

You cannot add different things together. This is true in life. Whereas 2 oranges plus 3 oranges is the same as 5 oranges, 2 oranges plus 3 apples remains 2 oranges and 3 apples. The former is the addition of the same things, and you can add them together, whereas the latter is a collection of different things, you can't add them.

 The same is true of mathematics. Adding a "one" and a "ten". You cannot say "we've got two "one" digits here, we'll add them together and get a 2 digit, because these "ones" are different things. The one in the "units" column signifies 1 unit, the one in the "tens" column signifies 1 ten. They are different things so you can't add them. The answer to the sum "ten plus one" is 11, a one in the tens column and a one in the units column, one ten and one unit, which is identical to the problem we started with. No addition has been done. Why? Because you cannot add different things together.

The English language obscures this fact, for example the number "twenty two" appears to be a unique number rather than a combination of two numbers... this is where the Germans have an advantage, in German it is made plain that 22 is a combination of two separate numbers, zwei und zwanzig, or two AND twenty is obviously a combination of two things and not a unique individual number.