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realmax + 1 infinity?

Asked by veloamoureuse on 11 Apr 2019
Latest activity Commented on by Jan
on 11 Apr 2019
Hello!
How come is realmax + 1 not inifity when typed into command window?
Thank you.

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2 Answers

Answer by Stephen Cobeldick on 11 Apr 2019
Edited by Stephen Cobeldick on 11 Apr 2019
 Accepted Answer

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.

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Jan
on 11 Apr 2019
Thanks Stephen, I've overseen teh "not" in the question.

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Answer by Steven Lord
on 11 Apr 2019

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.

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