Science & Mathematics Unanswerable questions

[Pie eyed]

It's a mathematical abstraction. Reasoning is often given as thus:
10^3 = 1 x 10 x 10 x 10 (= 1000)
10^2 = 1 x 10 x 10 (=100)
10^1 = 1 x 10 (=10)
10^0 = 1

But who put the 1s there? Mathematicians. You could just as easily say:
10^3 means three 10s combine to make a product = 1000
10^2 means two 10s combine to make a product = 100
10^1 means one 10 combines to make a product = 10
10^0 means zero 10s combine to make a product = 0

and you'd be equally right, except it doesn't work with negative powers, eg. 10^-1. So what I would suggest is the 'power' notation denotes how many zeroes follow the 1 to the left of the decimal point. Then 10^0 does = 1, not because 0 is a number but precisely because it isn't.

The zeroth power logic makes mathematical sense but it's merely a form of notation. Zero is not a number. I doubt any mathematician would argue it is.

Pie-eyed was on the right track. The question 'how many nothings in something?' has no answer.

I missed the bulk of this so thanks for the vote of confidence.

 

[HarryTiger]

Zero isn't a quantity, or rather it represents the lack of any quantity.

But to say it's not a number.... you're trying too hard to be clever.

Is the sum of two numbers another number?

1 - 1 = a number??

 

[SJ]

Zero is a number, it is also an integer, end of story.

 

[GuzzLG]

Zero is the average of -1 and 1. If you want to go from -1 to 1 you have to pass through zero. If the temperature is freezing and warms up it goes through 0. It's not like when the temperature is 0 there is a lack of temperature.

Not really though, temperature is just a scale that could have started with any number as the freezing point. When you bring in scales of measurement then 0 has significance like with temperature, but in a purely mathematical sense I agree it has no value.

 

[Walesy]

Zero is the average of -1 and 1. If you want to go from -1 to 1 you have to pass through zero. If the temperature is freezing and warms up it goes through 0. It's not like when the temperature is 0 there is a lack of temperature.

Not really though, temperature is just a scale that could have started with any number as the freezing point. When you bring in scales of measurement then 0 has significance like with temperature, but in a purely mathematical sense I agree it has no value.

Yeah, you kinda killed your first statement with your second one. Temperature as we know it is simply a scale of numbers to measure against- where 0 = "the point that water freezes" and 100 = "the point that water boils".

Absolute zero is a different kettle of fish.

1/0 <> infinity. 1/0 is NaN. Dividing by zero is meaningless- but that alone doesn't prove that 0 is not a number. 0 is a number, it's just not a quantity.

 

[Brad Roo]

Zero is a number, it is also an integer, end of story.

Please feel free to card any posts to the contrary.

 

[Pie eyed]

Absolute zero is a different kettle of fish.

We're getting very, very close to achieving absolute zero in laboratory conditions.

On Zero being a number.
It seems most are struggling with the concept that zero is not only a true number but an "even" number.
The confusion seems to come from the trouble reconciling zero with the natural numbers 1,2,3,4,5,6, etc.

I don't see that the negative numbers are any less conceptually confusing than zero as they are in practicality just as unobservable.

Numbers, basically are the notation of counting.


What I mean in simple terms is you can see 1 apple.
You cannot see 0 apples.
By the same token though you cannot see -1 apple either.



A couple of quotes regarding zero.

Indian mathematicians first came up with the number idea around 650 AD. Originally, perhaps as early as 200 AD, they used zero as a placeholder in another number. For example, in our notation: 216 is a different number than 2016. This use of zero advanced trade, commerce, and bookkeeping but does not qualify zero as a number. Zero, in its place-keeping function, is a kind of punctuation mark to help us interpret numbers correctly.

Zero is a number, by definition and the rules of arithmetic. Add zero to any number and you obtain that number.

Who discovered Zero?

http://www-groups.dcs.st-andrews.ac.uk/~history/HistTopics/Zero.html

 

[HarryTiger]

On Zero being a number.
It seems most are struggling with the concept that zero is not only a true number but an "even" number.

No we/they are not, most posters have shown a very good understanding of the situation. You're just saying say to sound more clever.

Numbers, basically are the notation of counting.

What I mean in simple terms is you can see 1 apple.
You cannot see 0 apples.
By the same token though you cannot see -1 apple either.

Captain O stuff here, there's no such tangible thing as a -1 apple but that point doesn't render the concept invalid. Numbers are for a lot more than just counting, they are for quantity representation where those quantities can be anything, not just real physical objects.

The only 'confusion' arises because people are asking the wrong questions.

Like "can I have 0 apples"?

Have means posess, and we don't usually talk of posessing nothing, we posess things. But that's just a semantic issue.

Phrase it in terms more mathematically appropriate and you see it is valid to have 0 apples.

Is the state of being of no apples a valid state?

*pulls out an empty fruit basket*

There you go, 0 apples.

A man pays for 10 apples from the fruiterer but picks out 11 apples.

How many more apples does the man need to pick out? (What's the difference between the correct amount and the amount he has picked?)

-1 Apples.

 

[carltonblue]

No we/they are not, most posters have shown a very good understanding of the situation. You're just saying say to sound more clever.



Captain O stuff here, there's no such tangible thing as a -1 apple but that point doesn't render the concept invalid. Numbers are for a lot more than just counting, they are for quantity representation where those quantities can be anything, not just real physical objects.

The only 'confusion' arises because people are asking the wrong questions.

Like "can I have 0 apples"?

Have means posess, and we don't usually talk of posessing nothing, we posess things. But that's just a semantic issue.

Phrase it in terms more mathematically appropriate and you see it is valid to have 0 apples.

Is the state of being of no apples a valid state?

*pulls out an empty fruit basket*

There you go, 0 apples.

A man pays for 10 apples from the fruiterer but picks out 11 apples.

How many more apples does the man need to pick out? (What's the difference between the correct amount and the amount he has picked?)

-1 Apples.

Last question in the brackets is worded wrong.

 

[Walesy]

The only 'confusion' arises because people are asking the wrong questions.

but... but...

If I have $12 and go to a fruit stand, how many mango's can I purchase if they are $3 each? (12/3=).

Now, if I went to the salvo's for a handout instead, but only had $1 to my name, how many free things could I get for my dollar?? (1/0=)

 

[HarryTiger]

but... but...

If I have $12 and go to a fruit stand, how many mango's can I purchase if they are $3 each? (12/3=).

Now, if I went to the salvo's for a handout instead, but only had $1 to my name, how many free things could I get for my dollar?? (1/0=)

But you aren't actually getting the free things "for your dollar", you're just getting them i.e. when you thrust your dollar out they refuse it.

According to the question you can get all the free things they have, or infinity if the supply is endless.

 

[Walesy]

But you aren't actually getting the free things "for your dollar", you're just getting them i.e. when you thrust your dollar out they refuse it.

According to the question you can get all the free things they have, or infinity if the supply is endless.

so 0/0 is infinity?

 

[HarryTiger]

It's a NaN, as other's explained.

f(x) = 1 / x

as x tends to 0 f(x) tends to infinity.


f(x) = 0 / x

is 0 for all non-zero values, as 0 never contains any quantity. (how many somethings are there in nothing?)

f() = 0 / 0

how many nothings are there in nothing?

 

[Brad Roo]

so 0/0 is infinity?

Close, you just need to ditch the backslash and join those zeros together.

 

[Pie eyed]

No we/they are not, most posters have shown a very good understanding of the situation. You're just saying say to sound more clever.



Captain O stuff here, there's no such tangible thing as a -1 apple but that point doesn't render the concept invalid. Numbers are for a lot more than just counting, they are for quantity representation where those quantities can be anything, not just real physical objects.

The only 'confusion' arises because people are asking the wrong questions.

Like "can I have 0 apples"?

Have means posess, and we don't usually talk of posessing nothing, we posess things. But that's just a semantic issue.

Phrase it in terms more mathematically appropriate and you see it is valid to have 0 apples.

Is the state of being of no apples a valid state?

*pulls out an empty fruit basket*

There you go, 0 apples.

A man pays for 10 apples from the fruiterer but picks out 11 apples.

How many more apples does the man need to pick out? (What's the difference between the correct amount and the amount he has picked?)

-1 Apples.

I'm revelling in the anonymous kudos to be earned on a forum...

As for the rest you just agreed with me...100%, which you may have intended?

 

[richoatthedisco]

Phrase it in terms more mathematically appropriate and you see it is valid to have 0 apples.

Is the state of being of no apples a valid state?

*pulls out an empty fruit basket*

There you go, 0 apples.

Also, 0 oranges.

So, apples = oranges.

 

[BACCS]

Zero.

If you really want a toughy from the maths field then the exact value of Pi?

0/0 is not zero, it is undefined (or infinite if you want to think of it in that way) as you are still dividing by 0. And pi.... 3.14169...

 

[BACCS]

It's a NaN, as other's explained.

f(x) = 1 / x

as x tends to 0 f(x) tends to infinity.


f(x) = 0 / x

is 0 for all non-zero values, as 0 never contains any quantity. (how many somethings are there in nothing?)

f() = 0 / 0

how many nothings are there in nothing?

Good answer.

 

[Wallaby]

If there were a billion monkeys typing at a billion keyboards 24 hours a day, they would eventually come up with something interesting.

Unfortunately, now we have the internet, we know it's not true.

 

[Fevola99]

If there were a billion monkeys typing at a billion keyboards 24 hours a day, they would eventually come up with something interesting.

Unfortunately, now we have the internet, we know it's not true.

the monkeys with the typewriters don't know what they're doing. they're just hitting keys and could eventually hit them in the right order to come up with something. people on the internet is a different scenario since they know the language and are actively trying

 

[Pie eyed]

0/0 is not zero, it is undefined (or infinite if you want to think of it in that way) as you are still dividing by 0. And pi.... 3.14169...

If you really want a toughy from the maths field then the exact value of Pi?

Come on someones going to do it eventually, why not you?

 

[SJ]

Come on someones going to do it eventually, why not you?

pi = 1/i * ln(-1)

 

[BACCS]

pi = 1/i * ln(-1)

Wouldn't that be undefined? ln(-1) isn't possible.

 

[Pie eyed]

pi = 1/i * ln(-1)

It'll be worth more than 6 goals if you can do it.

 

[melbournemartin]

It's a NaN, as other's explained.

f(x) = 1 / x

as x tends to 0 f(x) tends to infinity.


f(x) = 0 / x

is 0 for all non-zero values, as 0 never contains any quantity. (how many somethings are there in nothing?)

f() = 0 / 0

how many nothings are there in nothing?

Good ole L'Hospital can come in handy with the last one.

You know the old saying that a monkey with a keyboard, given an infinite amount of time, would eventually type out the entire work of Shakespeare. Well, we were given an algorithm to compute how long it'd take for the monkey to type out just a 8 or so letter word (not every 8 letter word is the same though). Believe me, it was a LONG time.