perhaps add a pic to show the examples.

This is maybe something we dont think about too much and is more of a curiosity.

In the following examples, i am subracting the lower number from the upper number although

not showing the minus sign. I do show the 'line' under the lower number that we sometime

put there just to keep things a little neater and so the result is just under that line.

The line is simply made with dashes for illustration:

-------

Ok, so starting with this first example:

009578

001119

---------

008459

Here we can start with the 8 and subtract 9, and doing so means we have to borrow 1 from the 7,

and so the result first digit on the far left is 9. The second is 6-1 because we borrowed from

the 7 reducting it to 6, and of course 6-1 is 5. Next we do 5-1=4 and 9-1=8 as shown, and just

fill in the two zeros in keeping with the form of the two numbers.

Thus we have completed the subtraction of 9578-1119=8459 and we are done with that example.

Now the next example isnt too much different:

1009578

1001119

----------

0008459

Here we started with the 8-9 and the borrow again, and so on and so forth, and when we get to the

two zeros we write them down like we did before. Finally we get to the far left digits 1 and 1, and

subtract them and get zero, and then write that down. We thus did the subtraction as before just

with three more digits.

Ok now for the final example, we do the following:

1009578

2001119

----------

_008459

We first subtract 8-9 as before and the borrow again and so on and so forth, and we get so far the

result shown below the line except we did not do the far left digits yet.

The question is, what do we do now?

I know there are other ways of doing this, but can you figure out a way to get the right result

in total using the procedure above except for that last far left digit pair and perhaps introduce

a second algorithm that corrects the result?

Not allowed here is to swap the numbers first cause we know already that works, this is a question

about doing it a different way.

Perhaps this is a good example of non communtative.