1 = 0,99........

[Bridge]

1)My point was that a computer is a more powerful calculator as it does much more things than a calculator, so I will leave this here.

2)I read your post. I agree that a computer cannot calculate infinite digits (like Pi as you said),but what I am trying to tell you is that it doesn't actually calculate them. It uses (let's say) mathematical tricks in order to get the result. It can't calculate Pi itself.

3)We just proved that it is the same number. It's like saying what's the distance from 2 to 2. Unless your are talking about complex numbers and not real numbers that statement doesn't make sense to me.

1) We can agree on that, but your wording made it sound like calculators are somehow more adept at math than computers. It's all based on implementation.

2) Yeah, but my point is it cannot store the data. Even if it can get the exact value of Pi through "mathematical tricks" it can not possibly store all of the digits. That way truly precise calculations of such complicated numbers is impossible.

3) Stephen Hawking also "proved" quite efficiently that the universe is not infinite but that's only because it cannot possibly be measured now. Laws are based around the knowledge we have at any given point in time, and laws have to be changed and revised constantly to accommodate new advances in science. Before the theory of relativity was developed for example scientists probably believed any speed attainable whereas now we know that anything with a positive mass is confined to speeds below the speed of light (e=mc^2). I don't doubt that 0.9~ is provably 1 but just like quarks are now measurable perhaps the real distance between 0.9~ and 1 will be measured at more than 0 in the future. Before quantum mechanics were invented, nobody would have imagined anything smaller than an atom but now we know that matter is constructed of particles even smaller than quarks.

All I'm saying is that it's possible we will be able to calculate the difference between 0.9~ and 1 some day; you even said it yourself: it's infinitely small. Maybe infinitely small today, but what about tomorrow?