realmax + 1 infinity?

Hello!

How come is realmax + 1 not inifity when typed into command window?

Thank you.

Answer 1

[Stephen23]

Because the value 1 is nowhere near the smallest value that can be added to realmax to create a new value. You would need to add a value that is more than half the difference between representable values around the magnitude of realmax. To get that value try using eps:

>> val = eps(realmax) % much bigger than 1.
val = 1.9958e+292
>> realmax + val/2
ans = Inf
>> realmax + val/3
ans = 1.7977e+308

This is exactly the same as if you add 1e-300 to 10: the answer is 10, because 1e-300 is nowhere near the difference in representable values around the magnitude 10, so adding 1e-300 makes absolutely no difference to the 10.

[Jan]

Thanks Stephen, I've overseen teh "not" in the question.

Answer 2

[Steven Lord]

If you handed Bill Gates or Scrooge McDuck a $1 bill, it doesn't change what he'll report for his net worth. A single dollar is negligible compared to how much money he has already.

Similarly, if you add 1 to realmax it doesn't change the value since 1 is negligible compared to realmax. If you want to know how much you'd need to add to realmax to make it not negligible, take a look at the eps function.