Daily Maths Problem #1

2

-2

Smartass.
There is no such number.

There are only five different numbers that always produce the same result after powering with them for any number of times.

1, 0, -1, inf, -inf

The results of all of them are different than 2.

My answer is: "it's a trap"

7

To answer this problem you need to grasp what infinity means

"to grasp what infinity means", you must not be a finite being, but a god.

Here is my counter offer.
Tell me your number!
If it is correct, I will give you 1 SBD. If it is wrong, you will admit that I won your contest.

To make it easier to you, I will only test 3 versions.

x^x^x^x^x = 2
x^x^x^x^x^x^x = 2
x^x^x^x^x^x^x^x^x = 2

If all three equations are true for your number, I will give you 1 SBD.
Any real number is a valid entry. It doesn't matter if it is a floating point or an integer. As long as it is a number, I will accept it.

Why am I even talking to you?
You don't even have the 5$ you promised as reward.

Im buyin it for the person who gives me the correct answer

But if you want Iwill give you the answer

Yep. Give it.
I am willing to lose 1 SBD if you are right.

The answer is root 2

As I expected - you are wrong.

Before trying to be smart, you should understand what equality means.
(It is a lot simpler concept than infinity.)
Your formula will never, ever be equal to 2. It will always be slightly less, even if you apply it infinite times.

Mathematicians assume equality, because it is almost the same, but that doesn't mean it is really true.

I repeat myself - there is no number other than the 5 I listed, that always produces a constant after powering with it.

if you use proof it technically equals root 2. Doing root 2 ^ of root 2 it will equal 1.9 recurring which technically equals 2.
x = 1.9recurring
10x = 19.9(rec)

10x - x = 9x = 18
x therefore = 2

I don't understand why you keep writing = instead of ~=
You want people to understand infinity but you don't understand equality.

A claim is either true or not.
In math there is no such thing as 'true enough'

If I am taking a test and write 2 instead of 1.9(9), it will be considered a wrong answer.

well you shouldnt be.

Fuck it!

Your answer isn't correct so I will NOT send you 1 SBD.

Instead I'll send you 0.99 SBD.
That is very close, but is not the same.

I'm sorry, he is right I think: in mathematic, 0.99999.... indefinitely is Equals to 1 (that's a mathematic professor who told us that...)

I disagree. There is a special sign for 'almost equal' that is ~= .
If the two were equal there would be no need for dedicated sign for these cases

no, but it's not almost equal: 0.999999999999 indefinitely is TOTALY equal to 1
like, not almost x)

Dude. I know it is not like that.
It is it is literally the reason for only weaker score I had on Math in middle school.

Mathematics is an exact science. Not almost exact, or technically exact. It is truly exact. An absolute science.

It doesn't matter if you write 'totaly' in all caps, or even if you use a bigger font.
If you don't have the exact same values on both sides, than you can't use the equal sign. It is wrong.

Man, i assure you that 0.9999999 indefinitely is equal to 1.
About the bigger front, I don't understand what you're talking about x)
And I studied math since I'm an engineer. And that's my mathematical professor in 2nd year of engineering that told us that.

If you think that you're better than him in mathematics, then I can't do anything for you.

Maybe try to search on web, there is plenty of proof for that... That is, if you can understand them :)

I don't need to be better than him.
This is not a complex type of math.
This is something that every fiftgrader studies.

There is = and there is ~= .

For every practical reason it doesn't matter. For computers it doesn't matter. Nor does it matter for engenders.

But the fact that it doesn't matter doesn't mean that it is the same. (There is no equality between these claims, just like there is no equality between 1 and 'not 1'.)

Btw - I am a software developer. I also work a lot with numbers.

https://en.wikipedia.org/wiki/0.999...

just see on wikipedia?

https://www.math.hmc.edu/funfacts/ffiles/10012.5.shtml

Or elsewhere if you don't trust wikipedia? :D

Admiting you're wrong can be good sometime :D

Damn, you are stubborn.
I would admit it if I was wrong. I am not.

Go and ask your teacher.
"How many different numbers are equal to the number 17?"

Ask yourself as well:
Is 16.9999(9)9 = 17?
Is 16.9999(9)9123 = 17?
Is 17.0000(0)01 = 17?

If what you are saying is true, than there are an infinite number of unique numbers that are equal to 17.
Say that outloud and think about how rediculous it sounds.

A number is either 17 or 'not 17'.

you don't understand what infinite is it seems...
anyway, you see mathematical proof but this isn't enough, so i can't say anything anymore :D
Just :

16.999999 indefinitely = 17
17.00000 indefinitely = 17
BUT
16.99999(9)123 != 16.9999 indefinitely != 17
so, no, there is only one 17, but you can write it a lot of different ways. But you can't understand and you don't want to understand, so... stay in your little life :D

That was my last message, no need to talk to someone that have no arguments and don't want to see the truth^^ it's like talking to a fanatic religious :D

So you are saying that there are 3 numbers equal to 17?
And then you claim that I am the fanatic?
:D

No, only one, since 17.0000000(0) and 16.99999(9) are basicaly equals to 17.
And thats not something you see

Remic is right

Thanks :) But I think he

@grubbyhat is completely right about the answer being square root of two.

To understand this, note that there is a difference between the situation with a finite number of operations and an infinite number of them.

There's that joke about an infinite number of mathematicians who enter a bar. "One pint of beer please", asks the first. "Half a pint", says the second, "One quarter, please", goes the third, "STOP!", says the barman and pours 2 pints for everyone. _{(This is the point where you laugh)}

The reason for this joke is that you can actually totally seriously consider the value of an infinite sum of the following form:

Any finite part of this sum will always be smaller than 2, but as the number of terms approaches infinity, the sum will get arbitrarily close to 2. At this point mathematicians would say that the limit value at infinity is, in fact equal to two.

Still with me?

Now consider the question about x^(x^(x ...). What this expression essentially denotes is the limit of the following sequence of numbers:

If @grubbyhat wanted to be extra mathematically precise, he could have written the problem in the following form:

(where denotes tetration, raising x to its own power n times, see this also).

It turns out that, indeed, if you choose root 2 for the value of x the corresponding limit will be equal to 2. You may check it numerically by increasing the number of terms and observing how the sequence approaches two.

To solve the problem, however, you do not even need to know much about limits. Instead simply observe that:

Because the power that the very first x is raised to is the same infinite sequence itself.

So technically you do owe @grubbyhat a SBD.

Check his wallet transactions, man.
Look a few days back.
I might not agree with you but I keep my word.
I gave you 1 SBD as much as I believed that all of you are correct.
(Meaning that I sent him 0.99 instead. :D)