What two numbers add up to 8001?

There are infinite combinations of two numbers that add up to 8001. Here are some examples using negative numbers:

-1 + 8002 = 8001
-2 + 8003 = 8001
-3 + 8004 = 8001
...

Here are some examples using two fractions that will add up to 8001:

8001/2 + 8001/2 = 8001
16002/3 + 8001/3 = 8001
24003/4 + 8001/4 = 8001
...

And here are some examples using two decimal numbers that will add up to 8001:

1.25 + 7999.75 = 8001
2.50 + 7998.5 = 8001
3.75 + 7997.25 = 8001
...

As you can see from the lists above, it can go on forever. However, when answering "What two numbers add up to 8001?", it may be more interesting to set some criteria to limit the result. We will set the follow criteria:

1) Only positive whole numbers can add up to 8001. (0 is not a positive or negative number and should not be included.)

2) Since a+b=29 is the same as b+a=29, we should only list it once.

Now, the answer to "What two numbers add up to 8001?" has 4000 answers:

1 + 8000 = 8001
2 + 7999 = 8001
3 + 7998 = 8001
.
.
3998 + 4003 = 8001
3999 + 4002 = 8001
4000 + 4001 = 8001

We have truncated the list above due to space, but you may be interested to know that we calculated the number of answers by dividing 8001 by 2 and then rounded down to the nearest whole number if necessary.

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