## defining a number as "real"

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- skeptical scientist
- closed-minded spiritualist
**Posts:**6142**Joined:**Tue Nov 28, 2006 6:09 am UTC**Location:**San Francisco

So elements of quantum groups are real numbers because they can be physically represented in the bizarre physics of the very small?

I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

"With math, all things are possible." —Rebecca Watson

- FiddleMath
**Posts:**245**Joined:**Wed Oct 11, 2006 7:46 am UTC**Location:**Madison, WI-
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I think that a lot of the basic ideas in this thread were discussed, fairly precisely and at length, in this thread, to which I'll link because I'm still quite fond of my little essay, there.

skeptical scientist wrote:Alky wrote:Formal definition:

http://en.wikipedia.org/wiki/Real_number

Layman's definition:

Any sequence of digits, with potentially infinite digits after the '.' but a finite amount before it, is a real number. Why the hell would they think 1 isn't a number? What number do you subtract from three to get two?

So 0.999... and 1 are different as real numbers because they are different as sequences of digits?

The definition does not say that DIFFERENT digit sequences are DIFFERENT reals; only that digit sequences ARE reals. It seems to me that this definition is equivalent to the limit of sequence of rationals.

Indiscreet Mathematics, a comic about maths

- skeptical scientist
- closed-minded spiritualist
**Posts:**6142**Joined:**Tue Nov 28, 2006 6:09 am UTC**Location:**San Francisco

Taejo wrote:skeptical scientist wrote:Alky wrote:Formal definition:

http://en.wikipedia.org/wiki/Real_number

Layman's definition:

Any sequence of digits, with potentially infinite digits after the '.' but a finite amount before it, is a real number. Why the hell would they think 1 isn't a number? What number do you subtract from three to get two?

So 0.999... and 1 are different as real numbers because they are different as sequences of digits?

The definition does not say that DIFFERENT digit sequences are DIFFERENT reals; only that digit sequences ARE reals. It seems to me that this definition is equivalent to the limit of sequence of rationals.

No, this definition is a lot more like defining a real to be a cauchy sequence of rationals. You need to have precise, correct definitions, otherwise when students get confused you have no one to blame but yourself.

I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

"With math, all things are possible." —Rebecca Watson

- skeptical scientist
- closed-minded spiritualist
**Posts:**6142**Joined:**Tue Nov 28, 2006 6:09 am UTC**Location:**San Francisco

Then you will become an outcast in the mathematical community and will have to beg for bread on the street.

I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

"With math, all things are possible." —Rebecca Watson

- EradicateIV
**Posts:**361**Joined:**Mon Mar 19, 2007 7:33 pm UTC**Location:**Brownsville, PA-
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TheLordOfPhysics wrote:if you can physically represent it it is real. like 1 being i have one bradpeice, two bradpeices and so on and so forth because i can physiclly represent it. were as negatives are representations of debt and owning "bradpeices's" if you will.

Hmm ... there is no such thing as pi breadpieces (even if you define a breadpiece to have some exact mass). So pi is not a "real" number?

- EradicateIV
**Posts:**361**Joined:**Mon Mar 19, 2007 7:33 pm UTC**Location:**Brownsville, PA-
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n3k5 wrote:So pi is not a "real" number?

You have to be careful on what you think is real. Your definition of real does not fit in with mathematics definition. It's like this in all fields, scientific or not.

Pi is a real number. It's hard to define what a real number is; however, easier to define what a real number isn't.

It's like telling your friends what the perfect wife is... you know she won't be a complete... Well, you get the idea.

1010011010

Our truth is only as good as our assumptions.

Our truth is only as good as our assumptions.

EradicateIV wrote:You have to be careful on what you think is real.

No I don't, I was talking about the definition of "real" in the original post. (Whatever that is *g* ... but that's the topic.)

Your definition of real does not fit in with mathematics definition.

I understand the mathematical definition, but I assumed it has already been agreen on here that that's not what we're talking about here. (N.B. I wrote ""real"", not "real".) I've said nothing about any other definition of my own, so any statements about that are meaningless ;-p

But seriously, I found the explanation of TheLordOfPhysics a bit incomplete, so I asked for a clarification. Not because I need to learn anything about real or "real" numbers, but just for the heck of it, to see what TheLordOfPhysics was getting at.

- EradicateIV
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- parallax
**Posts:**157**Joined:**Wed Jan 31, 2007 5:06 pm UTC**Location:**The Emergency Intelligence Incinerator

A "real" number is simply any number that's useful to think about. This probably includes all the integers and rationals, as well as all the algebraic numbers. By necessity, it would also include pi and e, and any other transcendental numbers that play a specific role in mathematics. You could probably get away with a contructionist definition such as "A "real" number is any number that can be defined by a finite statement."

parallax wrote:A "real" number is simply any number that's useful to think about. This probably includes all the integers and rationals, as well as all the algebraic numbers. By necessity, it would also include pi and e, and any other transcendental numbers that play a specific role in mathematics. You could probably get away with a contructionist definition such as "A "real" number is any number that can be defined by a finite statement."

You might like Computable Numbers.

- skeptical scientist
- closed-minded spiritualist
**Posts:**6142**Joined:**Tue Nov 28, 2006 6:09 am UTC**Location:**San Francisco

OneTrue wrote:parallax wrote:A "real" number is simply any number that's useful to think about. This probably includes all the integers and rationals, as well as all the algebraic numbers. By necessity, it would also include pi and e, and any other transcendental numbers that play a specific role in mathematics. You could probably get away with a contructionist definition such as "A "real" number is any number that can be defined by a finite statement."

You might like Computable Numbers.

Closer to his intention would probably be definable numbers.

"With math, all things are possible." —Rebecca Watson

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