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

[Ghieri]

3) Infinitely small, not non-existent.

You cannot measure something that's infinitely small. Infinitely small does not denote any kind of value, because it never stops getting smaller. Therefore it's the same thing.

In other words, you cannot measure the distance between .99~ and 1, because there isn't one.

[Robby]

3) Infinitely small

Da hell? How can something infinite be small?

Confusing topic is indeed confusing.

[Kreekakon]

Da hell? How can something infinite be small?

The definition of "infinity" basically means "anything", however big, or small that may be, which is also why it is mostly regarded as un-calculable.

[Robby]

After re-reading it, I somehow got it.

[Bridge]

When I say "infinitely small" I don't actually mean with an infinite amount of decimal places, I mean unmeasurable at this point.

Here is the Wikipedia definition of "infinitesimal":

"In common speech, an infinitesimal object is an object which is
smaller than any feasible measurement, but not zero in size; or, so
small that it cannot be distinguished from zero by any available means.
Hence, when used as an adjective, "infinitesimal" in the vernacular
means "extremely small". An infinitesimal object by itself is often
useless and not very well defined; in order to give it a meaning it
usually has to be compared to another infinitesimal object in the same
context (as in a derivative) or added together with an extremely large (an infinite) amount of other infinitesimal objects (as in an integral)."

All the proof you have is based around the flawed assertion that 1-0.9~ is 0. All of your calculations depend on this, and you provided no proof for this assertion. Occam's Razor dictates that the explanation that makes the least amount of unnecessary assumptions is the most efficient and most likely correct. I am not making any assumptions by saying 1-0.9~ > 0 because 0.9~ < 1. Prove without making any assumptions how it is not.

[Ghieri]

Until we find a way to measure an infinitely small number(Which in practical mathematics is an absurd concept) then the definition holds true.

[Bridge]

Until we find a way to measure an infinitely small number(Which in practical mathematics is an absurd concept) then the definition holds true.

EXACTLY. Because there exist no rules for these types of operations at this point, the math falls apart.

[BAndrew]

All the proof you have is based around the flawed assertion that 1-0.9~ is 0. All of your calculations depend on this, and you provided no proof for this assertion. Occam's Razor dictates that the explanation that makes the least amount of unnecessary assumptions is the most efficient and most likely correct. I am not making any assumptions by saying 1-0.9~ > 0 because 0.9~ < 1. Prove without making any assumptions how it is not.

I didn't make any assumptions.



Tell me where the assumption is.

[Ghieri]

Until we find a way to measure an infinitely small number(Which in practical mathematics is an absurd concept) then the definition holds true.

EXACTLY. Because there exist no rules for these types of operations at this point, the math falls apart.

How do you equate "Absurd concepts" with "no rules"?


Besides, it's been mathematically proven(See the limit above.)

[Bridge]

All
the proof you have is based around the flawed assertion that 1-0.9~ is
0. All of your calculations depend on this, and you provided no proof
for this assertion. Occam's Razor dictates that the explanation that
makes the least amount of unnecessary assumptions is the most efficient
and most likely correct. I am not making any assumptions by saying
1-0.9~ > 0 because 0.9~ < 1. Prove without making any assumptions how it is not.

I didn't make any assumptions.



Tell me where the assumption is.

lim n->nf {0.00 … 01} (n-1) …

Until we find a way to measure an infinitely small number(Which in practical mathematics is an absurd concept) then the definition holds true.

EXACTLY. Because there exist no rules for these types of operations at this point, the math falls apart.

How do you equate "Absurd concepts" with "no rules"?


Besides, it's been mathematically proven(See the limit above.)

Because we have no way of measuring numbers that small at this point in time. The difference between 0.9~ and 1 is immeasurably small, but it still exists. I don't consider it proven because the arithmetic operators +, -, * and / are designed to work with measurable numbers. As soon as you start using numbers that have no definite value the math stops working.