[Zer0]

Appalling gramme, it should be cannot, not "can't". You also cannot divide by 1 or anything beneath

Wrong on so many levels.
I can divide by a half perfectly well.
Five divided by half is ten.
(five divided in half is rather less than ten).

I can divide by one very easily indeed.
x/1=x

There's nothing wrong with "can't" as a word.

And it looks like you can't spell grammar- though it may be that you can't abbreviate "programme"


Presumably, you consider these statements of fact to be "repetitive antagonism"

Screenshot_2021-11-05-00-18-44-835_com.google.android.googlequicksearchbox.jpg (467.75 kB . 1080x2156 - viewed 3392 times)

Umm...unfortunately, the designer is Chinese.
Maybe it provides correct grammatical sentence construction if the language is changed/switched to " Mandarin ".
(I ain't interested in figuring that out, i consider it as a default in-built Calculator Application...We all can agree courteously that it ain't a Wren & Martin.)

Ps - If anyone wishes to write in to Xiaomi or call their 1-800 Number, Please go ahead.
🙏
I feel my Life, and of Others around me gets Alot more easy n comfortable, provided i can just
 " Let Go of Things, & Move On ".
(I shall stick to it)
😇

[Bored chemist]

Umm...unfortunately, the designer is Chinese.

Why is that unfortunate?

[Zer0]

Umm...unfortunately, the designer is Chinese.

Why is that unfortunate?

At the time when i purchased this android mobile phone...
China was making leaps & bounds progress in almost all sectors.
👍
I viewed China as a Pioneer & Visionary.
& no doubt The device beats all other competitors in design, coverage, computational power & is economically priced.

But then, Unfortunately, things changed pretty quickly pretty drastically internationally.
(Covid19, TikTok Spying, Chinese aggression in South China Sea, Neighborhood disputes, Hong Kong, Taiwan, Afghanistan, CCP moving towards (complete)Totalitarianism.)

I have lost my trust & faith.
👎

There are quite a few in-built applications that are uninstallable.
I cannot root the device, orelse warranty snaps, & of course the pandora's jar opens.
I check complete details before updating os & security patches.

Ps - In short, Now i truly understand, what it means & how it feels like, to be sleeping with the enemy.
🤞
(Sure, i can divorce it & remarry, but to carry on flirting with disasters is in my lame genes.)
😉

[Petrochemicals]

Appalling gramme, it should be cannot, not "can't". You also cannot divide by 1 or anything beneath

Wrong on so many levels.
I can divide by a half perfectly well.
Five divided by half is ten.
(five divided in half is rather less than ten).

I can divide by one very easily indeed.
x/1=x

There's nothing wrong with "can't" as a word.

And it looks like you can't spell grammar- though it may be that you can't abbreviate "programme"


Presumably, you consider these statements of fact to be "repetitive antagonism"

 [ Invalid Attachment ]

Umm...unfortunately, the designer is Chinese.
Maybe it provides correct grammatical sentence construction if the language is changed/switched to " Mandarin ".
(I ain't interested in figuring that out, i consider it as a default in-built Calculator Application...We all can agree courteously that it ain't a Wren & Martin.)

Ps - If anyone wishes to write in to Xiaomi or call their 1-800 Number, Please go ahead.
🙏
I feel my Life, and of Others around me gets Alot more easy n comfortable, provided i can just
 " Let Go of Things, & Move On ".
(I shall stick to it)
😇

You asked why I have my tag line, BC knows I do not respond but snipes anywhoo, that is why I have my tag line.

[Bored chemist]

BC knows I do not respond but snipes anywhoo,

You mean "BC still points it out when I says stupid things".

And we know what the tag line is for- it's to warn others that they also might suffer the terrible loss; you might put them on your ignore list too.

Do I look bothered?

[hamdani yusuf (OP)]

Hi.

I'm losing track of what was being discussed here. 
This bit I can do:

When does Ln(a) not exist?

   When a = 0.

Best Wishes.

What's the difference between something that doesn't exist and something that's not defined in math?

Imaginary number was once thought not to exist.

[Eternal Student]

Hi.

What's the difference between something that doesn't exist and something that's not defined in math?

    One is a personality and the other is a mermaid?

(I know that's one a bit old.  I don't get out much).    Anyway....   What did I mean when I said   Ln(a)  doesn't exist?
In this context I did mean that it isn't defined.

Best Wishes.

[Petrochemicals]

Did he snipe?

[Bored chemist]

Did he snipe?

No; he just stated the obvious.

[hamdani yusuf (OP)]

https://www.quora.com/What-is-0-0-the-zeroth-power-of-zero-1

This had previously been the subject of some debate in the mathematical community until Donald Knuth set things straight in 1992, so it’s understandable that some confusion lingers, but the modern convention is to define  0⁰=1 , for good reason.

https://www.quora.com/How-can-we-prove-0-0-is-equal-to-one

A definition cannot be “proven” right or wrong. That doesn’t even make sense.

It might appear that the “theorems”  x⁰=1  and  0^x=0  contradict each other in a way that forces us to leave  0⁰  undefined. But  0^x=0  cannot actually be a theorem, even if we ignore the  0⁰  case: everyone agrees  0^x  is not defined for any negative  x . It can’t be, because that would break the theorem that  b^x⋅b^−x=1 .

So there are good reasons for wanting to define  0⁰=1 , but does it break anything the way defining  0/0  would? In fact it doesn’t. All the usual laws of exponentiation remain valid with this definition.

That’s what we mean when we say that the choice to define  0⁰=1  is the right one.

[Eternal Student]

Hi.

This had previously been the subject of some debate in the mathematical community until Donald Knuth set things straight in 1992, so it’s understandable that some confusion lingers, but the modern convention is to define  00=1 , for good reason.

    I don't think there's a thing like the Oxford English Dictionary for Mathematics,  somewhere that the very latest terminology and conventions are recorded and will be recognised as the definitive reference.  So Donald will have a bit of trouble getting everyone to adopt that convention.

   I Googled for "official mathematical conventions" and didn't find anything useful.   I did find an extremely long and detailed booklet produced by  ETS  (Education Testing Service) which seems to be used as the standard for many examinations in the United States.
   https://www.ets.org/s/gre/accessible/GRE_Math_Conventions_18_point.pdf.
   On page 9 of 31    they  write:   Because all numbers are assumed to be real, some expressions
are not defined. Here are three examples:  .........
Example 3:  0⁰  is not defined. 

     This was produced in 2010, so about 18 years after Donald had apparently set the precedent that 0⁰ will always be 1.

    Anyway, defining 0⁰ = 1 is something you can do and it obviously helps to keep things like power series written in a convenient form (just like the convention 0! = 1 ).   It's certainly been an un-official convention for a long time.   Just be careful if you write it in an examination where they aren't using that convention and be extremely careful if you ever obtain an expression like 0^x  ,or   x^y  and  need to examine the limiting behaviour as x→0  and/or y→0.

Best Wishes.

[Zer0]

Did he snipe?

Did he snipe?

No; he just stated the obvious.

ROFL!
🤣
I find myself  rather precariously positioned between you two.
😔
I'd Request you both now to humbly forgive Me & kindly let me move on.
🙏

Throughout life, i have been corrected and put inline on various occasions by various Individuals.

I'm a bit Sensitive, and have sometimes disagreed with the ways in which Knowledge was imparted to me.

But I'm also a bit Sensible, hence mostly been appreciative that Knowledge was passed over to me.

An avid sweets trader was making the rounds. Going from village to village, selling his products.
🍭
As afternoon arrived, he decided to rest under the shades of a banyan tree.
🌳
As he was quite exhausted, soon he fell asleep, dreaming on the sweet profits he was generating.
😴
Only to be abruptly woken up by a Sage. Who seemed to be a venting in anger for reasons unknown.
😠
The Sage went on a rampage, thrashing the Trader left right & centre. Mostly targeting the trader's stomach.
🤛🤜
The Trader, a pious individual, had never before seen or known his molester, & kept on asking for forgiveness & begging for the beating to Stop!
🙏
As the Trader fell to the ground, the Sage trampled upon his stomach.
Immediately the Trader started vomiting, & lo & behold, A lil Snake sneaked out from the Trader's mouth.
😲
The Sage stopped, sat besides the Trader in a consolatory manner & explained...

As he was passing by, he saw the Trader resting with his mouth open.
Right about then, a lil snakelet made it's way right through inside.
     Sage further explained, there was no time to wake up the Trader in an orderly manner, & no way to explain to the Trader what had just happened, considering the trader might have had a heart failure by fear, just knowing a snake had crawled inside of him.
Hence the Sage had to be decisive and act in time with brutality.
🐍

When the Trader Realised all that had happened...he fell onto the Sage's feet.
Thou pretty sensitive and in pain from the beatings, but alot more sensible to foresee what he had gained in return for a lil bit of bashing...his Life.
😇

All Sages have different ways of dealing with the Snake of Ignorance within Us.
✌️
& All Traders are not as appreciative. Humans just follow Logic, but are controlled by Emotions.


Ps - Wish to Apologize to the OP for hijacking it & taking it to a place where it clearly does Not belong.
I'm Sorry Yusuf.
I shall stop now.
🙏

[hamdani yusuf (OP)]

On page 9 of 31    they  write:   Because all numbers are assumed to be real, some expressions
are not defined. Here are three examples:  .........
Example 3:  0⁰  is not defined.

Following the premise above,
√(-1) would be undefined. Further implications are:
Euler's identity doesn't exist.
Wave equations don't exist.

Argument from authority has no weight in scientific debates.

[Bored chemist]

"What's 0^0 ?"
When will it matter?

[Eternal Student]

Hi.

Argument from authority has no weight in scientific debates.

   By argument, I hope you mean discussion.  I'm fine with you defining 0⁰ =1  if you want to. 

   I'm genuinely surprised that there isn't an official list of mathematical conventions and symbols.... but there just doesn't seem to be.   There is one for house building regulations, words in the English Language, Electrical engineers have various recognised industry standards   etc.   However, Maths doesn't seem to have anything like this.

Best Wishes.

[hamdani yusuf (OP)]

"What's 0^0 ?"
When will it matter?

When the answer is necessary to solve our problem.
There were time when negative numbers didn't matter. There were also time when imaginary numbers didn't matter.

[hamdani yusuf (OP)]

   By argument, I hope you mean discussion.  I'm fine with you defining 0⁰ =1  if you want to.

The word discussion is more suitable to replace the word debate. The argument from authority itself is a widely known logical fallacy.
https://en.wikipedia.org/wiki/Argument_from_authority

In this discussion, one side think that 0⁰ is defined. The other side think that it's undefined. We try to convince the other side that our thought is better than the other. Many mathematical proofs are in the form of reductio ad absurdum, i.e. following the implications of an assumption to the point of absurdity/contradiction, to conclude that the assumption is false, hence we choose its opposite. 
Arguing that our position is better because it's supported by an authoritative body can be useful in cases where each sides of the discussion have inadequate capacities to gather and process necessary data to produce correct and reasonable conclusions. Laymen discussion on complex problems like climate change or how to handle a pandemic are often cited as examples. Statements from the authorities can save our time and energy.
But if the goal is to find the fundamental truth, we need to process the raw data ourselves, and determine why a position is better than the other without relying on what the authority said.

[Eternal Student]

Hi again.

The word discussion is more suitable to replace the word debate.

  OK.

   Perhaps I wasn't making myself clear.  I'm not arguing with you in the sense of deliberately being unpleasant, or I certainly wasn't intending to do that anyway.  It's always been a discussion as far I'm concerned.

   As regards quoting authority, the most important point is that it isn't in my power to change the conventions.   There doesn't even seem to be a place or document where current conventions, notation and terminology for Mathematics is recorded and provides a standard for the world.   We could write a letter of complaint but I don't know where to send it.

   If it's important to you then you have my support.  It's a useful convention to have 0⁰ = 1  it makes a fair level of sense and it certainly makes it easier to write out power series  like 

  P(x) =     in one neat formula (which is commonly done) instead of writing something like this....

  P(x) = a_o  +

Or resorting to the use of two lines and splitting the definition of P(x) like this....


P(x) =    

 - - - - - - - - - - - - - - - -

But if the goal is to find the fundamental truth, we need to process the raw data ourselves, and determine why a position is better than the other without relying on what the authority said.

   Yes, seems like good advice.
You're actually doing amazingly well working through all the complications of defining what exponentiation should mean.
How (and why) will we define  0 raised to an irrational power,   like  0^π  ?   I honestly don't know.  Most people would just take a rational sequence {x_n} tending to Pi   and look at the limit of  0^x_n  - but what would you do and why?

Best Wishes.

[Bored chemist]

"What's 0^0 ?"
When will it matter?

When the answer is necessary to solve our problem.
There were time when negative numbers didn't matter. There were also time when imaginary numbers didn't matter.

If the answer to 0^0 will solve our problem then the solution to the problem will tell us the answer.

However, in the same way that there's no useful problem that involves calculating 1/0- because the answer is undefined- there can be no useful problem that involves calculating 0^0.

[hamdani yusuf (OP)]

However, in the same way that there's no useful problem that involves calculating 1/0- because the answer is undefined- there can be no useful problem that involves calculating 0^0.

https://www.quora.com/What-is-0-0-the-zeroth-power-of-zero-1
And so we now assign  0^0  the value that’s useful, which is  1 . Why is that useful? Because it lets us manipulate exponentials without adding special cases.