Dimensions

I want to come back to this binary 0-1 matrice in artificial data processing. It seems fundamental but is it a natural function?

Where and how would nature make use of a binary function?

 

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No, zero is NOT defined as having no value. It is defined as having a very specific value, depending on the context. Zero degrees (Celsius or Fahrenheit) IS a value. It is halfway between the value of 1 and the value of -1.

 

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You mean that one definition of zero is: the number between the set of all negative numbers and the set of all positive numbers.

The number itself has no value. It can act as a placemat for a countdown; 3, 2, 1, go!

I cite the main definition that zero is: the arithmetical symbol 0 or 0̸ denoting the absence of all magnitude or quantity.

Adding 0 to a number leaves its same. 0 is called the additive identity and the property is called the additive identity property.

4 + 0 = 4

0 + 3 = 3

Multiplication property of zero

Zero times any number is equal to zero. Which means, multiplying any number by 0 gives 0.

0 × 7 = 0

2 × 0 = 0

Multiplication property of one

Multiplying any number by 1 leaves it unchanged. 1 is called the multiplicative identity hence the property is called multiplicative identity.

1 × 36 = 36

23 × 1 = 23

Exponents of one

The number one raised to any power is always one.

1100 =1

1-34 =1

Exponent one

Any number raised to power one remains unchanged.

31 = 3

-51 = -5

Exponents of zero

The number zero raised to any power is remains zero.

024 = 0

0-9 = 0


Zero as numerator

Zero divided by any non-zero number is zero.

0 ÷ 3 = 0

0 ÷ 6 = 0

Zero as denominator

Any division by zero is not defined

9 ÷ 0 = not defined Because 0 has no definitive value

3 ÷ 0 = not defined Because 0 has no definitive value

0 ÷ 0 = 0

 

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Oh look. A giant copy-paste splooge of generic dictionary definitions of buzzwords vomited up by the Write4Ubot. How unexpected.

In fact, it's so unexpected, my template for it - which I made more than three years ago - is still just as relevant

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Does a blank DVD have nothing on it? Is it a string of zeros?

Is blank, with a DVD a useful kind of nothing, in that having nothing on it means you can put something on it, and yet, it's still a DVD?
The symbol for zero, 0, isn't nothing; nothing would be no symbol.

If you say 0 means nothing, that's ok as long as you mean mathematically, and really, strictly in a counting sense. Or maybe that's just me.

 

It has a string of flat spans and depressions in it that we humans have - purely as an arbitrary convention - assigned the labels "zero" and "one".

That application of the concept of zero (and one) to a physical state is quite a sophisticated mechanism of abstraction; one that only humans - and only modern humans at that - can conceive.

 

No, it has nothing (zero information) on it. It is a blank disk.

[/quote]Is blank, with a DVD a useful kind of nothing, in that having nothing on it means you can put something on it, and yet, it's still a DVD?
The symbol for zero, 0, isn't nothing; nothing would be no symbol.[/quote] Other than its formatting data, it has no informational data.

Yes, it is the mathematical definition. However it used as a placemat for other calculations.
IOW in double entry bookkeeping zero in both debit and credit column indicates the book is in balance.

 

No, I meant what I said. I gave you an example and you quoted it.

Of course it does. It has a value as much as 1 degree or -10 degrees has a value

I'd call that a poor definition. Zero is a specific quantity, not the absence of quantity.
.

 

In the olden days, when computer data was stored on cassette tapes, a one was an audible tone and a zer0 was a different audible tone. The read head would detect one (completely arbitrary) tone and arbitrarily call it a zero - and it would detect the other (completely arbitrary) tone and arbitrarily call it a one. As far as I know, floppy disks did it the same way. CDs and DVDs use pits that reflect a laser in a different way than the spans between the pits. Bar codes use bars which reflect a laser differently from the spaces between the bars.

Those "physical" zeroes are clearly not "nothing".

 

This is why I wonder if W4U is a bot that doesn't really understand what it's saying.

Citing one meaning is a red herring; it doesn't negate all the other meanings.

In an example that has been pointed out several times, zero Celsius certainly has a magnitude and quantity.

 

And it was correct . I quoted the formal definition of that algorithm.
To wit:

No, that is stretching it.

But zero has no magnitude.

https://physics.stackexchange.com/questions/548172/order-of-magnitude-of-zero#

But all this is theoretical mathematics for human convenience. In nature zero is the absence of a property or (countable) value. Besides for purposes of this discussion, zero dimension means absence of dimension.

 

False. You have confused two things: magnitude and order of magnitude.

The value 1 has a magnitude of one, but an order of magnitude of zero.
The value 10 has a magnitude of ten, but an order of magnitude of one.
The value 0 has a magnitude of zero, but an order of magnitude that is not defined.

 

But I didn't mean what you said I meant.

Zero does have a magnitude on a temperature scale. It's magnitude is one (arbitrary) degree lower than 1 degree and one (arbitrary) degree higher than -1 degrees.

All mathematics is for human convenience.

There is no zero in nature. Zero is an entirely made-up human construct. You're still confusing zero with nothing.

 

I was going to mention the same thing myself.

 

All symbolic mathematics is for human convenience. Generic universal mathematics are an inherent function of spacetime geometry.

Is spacetime real, or is it a mathematical construct?

.....

https://physics.stackexchange.com/q...a-mathematical-construct-and-not-a-real-thing

 

And here we are, finally, back at Write4U's religion, which is where he has been trying to drag this thread for the last several pages.

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Here comes the spoilsport!

This thread has been off topic for the last several pages about the meaning of zero, a mathematical symbol, which is only tangentially related to "dimensions" such as vectors and scalars.
I have drawn attention to that fact, so don't try to hang this on me, please.

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In mathematics, the dimension of a vector space V is the cardinality of a basis of V over its base field. It is sometimes called Hamel dimension or algebraic dimension to distinguish it from other types of dimension. https://en.wikipedia.org/wiki/Dimension_(vector_space)#

Is dimension a vector or scalar?

https://www.quora.com/Is-a-one-dimensional-vector-a-scalar

Moreover, mathematics is part of science, not religion. As a scientist I am sure you have used mathematics religiously yourself, no? Do you pray to it? I don't.

p.s. '"zero" (0) was introduced by the originator of this thread in post #4

 

Indeed. He has once again mistaken the map for the territory.

Pulling from an amateur's post on stackexchange, he has interpreted the phrase "Spacetime is, from a mathematical viewpoint, a manifold, which is a set of points" literally.
He thinks is means the map (a manifold) is the same thing as the territory (spacetime).

And, since I'm pretty sure he's got me on Iggy, he's going to continue to look foolish indefinitely.

Reported.

 

Well, seems to me the following analysis seems to disagree with your perspective.

https://cmci.colorado.edu/classes/INFO-2301/files/practice_2-1-19.pdf

 

That's just your unsupported belief, isn't it?

Spacetime is real and a sugar cube is real. The mathematics that describes them is a human construct, just like the English words that describe them are a human construct.