We often view "1+1=2" as a fact. But...
Many times 1 + 1 is not 2. On the light side you can add one rabbit to one rabbit and end up with a whole rabbit family.
You can also add a piece of string to another piece of string - and just get a longer piece of string. And adding one chaos to another chaos will most likely only get you bigger chaos. Not two chaoses. (Thanks, @seabird20)
If you read two newspapers you don't get twice as much news. Sometimes the information cancels out altogether (Thanks, @richardveryard)
And one hull plus one hull are not always two hulls. Sometimes it is a catamaran.
Back to the "serious math"...
1+1=10 if we do it in binary number system.
And if we have a clock-system with the "hours" 0 and 1 only the "1+1" will become "0". (Just like 08:00 plus 9 hours will become 5...)
And we also need to pay attention to what "+" means. How we use "+" to add number is a rule in the number system we have agreed upon.
And what number system are we using? Is the "1" belonging to the set of N or Z? Or real numbers? Are the first "1" the same as the second "1".
When using computers and Float numbers 1 + 1 do not always add upp to 2, due to representation of floating numbers.
So, very seldom is 1+1 = 2
And by the way. If you have one hungry lion and add three rabbits you will not get four live animals. You will get ONE less hungry lion.
To see that 1+1 is anything but 2 can be very advantageous. If you only find "2" as the right answer you miss a lot of opportunities....
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great post philosophy of math is an amazing thing. Once we reflect upon numbers we realize that math is just a construct that is created by man and then we all agree upon the rules. For example the square root of -4 is i2 imaginary 2. What other evidence do you need to illustrate that math is much like existence. We as a species have all agreed to certain rules and procedures and we follow these rules. What innovation processes do is discover and play with the thought that some do not abide by all the rules of reality constructs and choose to view differently. Once we lock ourselves into the 1+1= always equals 2. you lock a reality (that does not exist) into your personal procedures.
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