# Opinions on infinitely close things?

Gold Member
What are your opinions on infinitely close objects / numbers?
I believe in them, because I can say 3.9 is close to four, but 3.999 is as well, and so is 3.99999999.
I've heard of LOTS of scientists who disagree with this, can anyone prove this wrong (or right)?

#### CompuChip

Homework Helper
I would agree that 3.9 is close to four, and 3.999 is closer to it even, but no finite amount of 9's will make it equal to four.

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#### jbunniii

Homework Helper
Gold Member
The distance between two nonequal real numbers is a positive real number. Since there is no smallest positive real number, there is no number $x$ "infinitely close to" $y$ with $x \neq y$.

Proof that there is no smallest positive real number: you supply your candidate $x > 0$, I'll respond with $x/2$.

#### economicsnerd

It depends on how you define "number".