What two numbers add up to 4099?

There are infinite combinations of two numbers that add up to 4099. Here are some examples using negative numbers:

-1 + 4100 = 4099
-2 + 4101 = 4099
-3 + 4102 = 4099
...

Here are some examples using two fractions that will add up to 4099:

4099/2 + 4099/2 = 4099
8198/3 + 4099/3 = 4099
12297/4 + 4099/4 = 4099
...

And here are some examples using two decimal numbers that will add up to 4099:

1.25 + 4097.75 = 4099
2.50 + 4096.5 = 4099
3.75 + 4095.25 = 4099
...

As you can see from the lists above, it can go on forever. However, when answering "What two numbers add up to 4099?", 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 4099. (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 4099?" has 2049 answers:

1 + 4098 = 4099
2 + 4097 = 4099
3 + 4096 = 4099
.
.
2047 + 2052 = 4099
2048 + 2051 = 4099
2049 + 2050 = 4099

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 4099 by 2 and then rounded down to the nearest whole number if necessary.

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