Maths query

[CheeseSlice]

Depends what you mean by 0.99999, equals, recurring and 1

HTH BIDI

Ah jolly good, this can be resolved with a Bill Clinton-esque answer.

It depends what you're definition of 'equals' equals...

[Doggy Styles]

Ah jolly good, this can be resolved with a Bill Clinton-esque answer.

It depends what you're definition of 'equals' equals...

As the OP, I intended 'equals' to mean 'exactly the same thing'.

Not 'equivalent to'.

What gnaws away is that an infinitesimally small difference is still an entity and therefore should not be ignored.

[expat]

As the OP, I intended 'equals' to mean 'exactly the same thing'.

Not 'equivalent to'.

What gnaws away is that an infinitesimally small difference is still an entity and therefore should not be ignored.

The foundation of mathematics consists of rules for saying that 2 things that are not exactly the same thing, are (or are to be treated as) the same thing within the specific sphere of discourse.

Isomorphism is the only handle on understanding the conceptual universe.

[d000hg]

As the OP, I intended 'equals' to mean 'exactly the same thing'.

Not 'equivalent to'.

What gnaws away is that an infinitesimally small difference is still an entity and therefore should not be ignored.

How do you define "equivalent to" and "exactly the same"?

[OwlHoot]

Depends what you mean by 0.99999, equals, recurring and 1

HTH BIDI

"0.999.. recurring" is shorthand for "the limit of the infinite sequence {0.9, 0.99, 0.999, ...}", and that limit is 1.

So, yes, the two are one and the same.

(The limit of a sequence needn't be a member of the sequence.)

[Doggy Styles]

How do you define "equivalent to" and "exactly the same"?

"Treated as the same thing" and "is the same thing".

[d000hg]

Define "is".

[NotAllThere]

There is no number (in the real number system, with standard analysis) between 0.99999.... and 1. Therefore 0.99999... and 1 are simply different representations of the same number.

Anyone who says different either doesn't know what they're talking about or is using non-standard analysis. I suspect strongly the former.

[expat]

There is no number (in the real number system, with standard analysis) between 0.99999.... and 1. Therefore 0.99999... and 1 are simply different representations of the same number.

Anyone who says different either doesn't know what they're talking about or is using non-standard analysis. I suspect strongly the former.

Most likely the former. Few who know what it takes to have a system where they are not equal would be able to resist showing that they know.


Expat's Awkward Axiomatic Arithmetic:
AXIOM 1: there are only two numbers, 1 and 0.999999...
AXIOM 2: 1 = 1 and 0.999999... = 0.999999...
Rule of Inference: if a relation is not axiomatic, it is false.
Derived rule: it is false that 1 = 0.999999...

Admittedly you can't do much with it, except possibly deduce that I did Mathematical Logic rather than Analysis.

[expat]

"Treated as the same thing" and "is the same thing".

Two things can not be exactly the same thing in all respects; otherwise they are not two things, it is one thing mentioned twice.