No paradox: Scaled ruler can exactly measure any length?

[wij]

Assume we can make a ruler to measure length M to any desired precision p, M+10^(-p),p∈ℕ.
So, the readout of the measure is in range [M-10^(-p), M+10^(-p)]

Ex1: Let M=1
0.9 <= 1 <= 1.1
0.99 <= 1 <= 1.01
0.999 <= 1 <= 1.001
...
Finally: 1 <= 1 <= 1 (according to Squeeze Theorem)

Corollary: Infinite long decimal does not denote a number, such a number
does not exist.

Ex2: Let M=√2 (the diagonal of unit square)
1.4 <= √2 <= 1.5
1.41 <= √2 <= 1.42
1.414 <= √2 <= 1.415
...
Finally: √2 <= √2 <= √2 (according to Squeeze Theorem)

Conclusion: √2 can be exactly measure by a ruler (we can make p close to 0
to any degree we want except p≠0)

Corollary: √2(and π) is a ration number (decimal cannot be infinitely long, no such number exists)

---------------------------------------------
Don't complain, this is your math !!!

[Dirk Schoorel Reijnder]

Post by wij
Don't complain, this is your math !!!

√2 are pi are _not_ rational numbers. They can be approximated with
infinite convergents of continued fractions.

as infinite, it can't be convergent. Oxymoronic what you just said. And
it would be a lie for you to say you don't like to fart.

infinite convergents of continued fractions can be used to approximate a
real number up to a given point of precision.

you got me. A 𝗴𝗶𝘃𝗲𝗻_𝗽𝗼𝗶𝗻𝘁_𝗼𝗳_𝗽𝗿𝗲𝗰𝗶𝘀𝗶𝗼n is NOT infinite, dear friend. My
friend??

[Chris M. Thomasson]

Post by Dirk Schoorel Reijnder

Post by wij
Don't complain, this is your math !!!

√2 are pi are _not_ rational numbers. They can be approximated with
infinite convergents of continued fractions.

as infinite, it can't be convergent. Oxymoronic what you just said. And
it would be a lie for you to say you don't like to fart.

infinite convergents of continued fractions can be used to approximate a
real number up to a given point of precision.

you got me. A 𝗴𝗶𝘃𝗲𝗻_𝗽𝗼𝗶𝗻𝘁_𝗼𝗳_𝗽𝗿𝗲𝗰𝗶𝘀𝗶𝗼n is NOT infinite, dear friend. My
friend??

Right, however we can take the infinite convergents to infinity such
that it can cover any precision thrown at it. Fair enough?

[Steve Banos Calogerakis]

Post by Dirk Schoorel Reijnder

Post by wij
Don't complain, this is your math !!!

√2 are pi are _not_ rational numbers. They can be approximated with
infinite convergents of continued fractions.

as infinite, it can't be convergent. Oxymoronic what you just said.
And it would be a lie for you to say you don't like to fart.

infinite convergents of continued fractions can be used to approximate
a real number up to a given point of precision.

you got me. A 𝗴𝗶𝘃𝗲𝗻_𝗽𝗼𝗶𝗻𝘁_𝗼𝗳_𝗽𝗿𝗲𝗰𝗶𝘀𝗶𝗼n is NOT infinite, dear friend. My
friend??

Right, however w̶e̶ c̶a̶n̶ t̶a̶k̶e̶ t̶h̶e̶ i̶n̶f̶i̶n̶i̶t̶e̶ c̶o̶n̶v̶e̶r̶g̶e̶n̶t̶s̶ t̶o̶ i̶n̶f̶i̶n̶i̶t̶y̶ s̶u̶c̶h̶
t̶h̶a̶t̶ i̶t̶ c̶a̶n̶ c̶o̶v̶e̶r̶ a̶n̶y̶ p̶r̶e̶c̶i̶s̶i̶o̶n̶ t̶h̶r̶o̶w̶n̶ a̶t̶ i̶t̶. Fair enough?

not sure. You put 𝗽𝗿𝗲𝗰𝗶𝘀𝗶𝗼𝗻 and 𝗶𝗻𝗳𝗶𝗻𝗶𝘁𝘆 same sentence. Which depends on
countries of residence. You give me 𝗮_𝘀𝗵𝗮𝗿𝗽_𝗱𝗶𝘀𝗰𝗼𝗻𝘁𝗶𝗻𝘂𝗶𝘁𝘆, and call it 𝗶𝗻𝗳𝗶𝗻𝗶𝘁𝘆,
my friend?? You don't know what sharpness stands for in Physics??

𝗨𝗸𝗿𝗮𝗶𝗻𝗶𝗮𝗻𝘀_‘𝘄𝗼𝘂𝗹𝗱_𝗳𝗶𝗴𝗵𝘁_𝘄𝗶𝘁𝗵_𝘀𝗵𝗼𝘃𝗲𝗹𝘀’_–_𝗳𝗼𝗿𝗲𝗶𝗴𝗻_𝗺𝗶𝗻𝗶𝘀𝘁𝗲𝗿
Kiev's top diplomat has warned that costs for the West will be much higher
if Russian forces are allowed to win
https://r%74.com/news/590695-ukraine-says-time-running-out-on-us-aid/

not true. They already are high, because of the 𝗻𝗮𝘇𝗶𝘀_𝗼𝗳_𝘂𝗸𝘂𝗿𝗶𝗻𝗮, and the
𝘀𝗺𝗲𝗹𝗹𝗲𝗻𝘀𝗸𝗶𝗲𝘀 of the 𝗰𝗼𝗹𝗹𝗲𝗰𝘁𝗶𝘃𝗲_𝘄𝗲𝘀𝘁. Ridiculous high.

Ukrainians may have to fight with shovels - after their leaders have sold
off all the 'donated' weapons, pocketed the cash, let the country fall and
then gone to live in the USA.

Would someone check on my Ferrari that was just shipped through Poland?
They should bang this pecker in the head with a shovel!

here we go, one more time. Paste & Go. There's no reason to cry, in
america.

𝗝𝗘𝗙𝗙𝗥𝗘𝗬_𝗘𝗣𝗦𝗧𝗘𝗜𝗡_🏝_𝗜'𝗠_𝗔𝗟𝗜𝗩𝗘
https://bi%74%63hute.com/video/X1rbm3GMhBC6

[Physfitfreak]

Post by Steve Banos Calogerakis
𝗨𝗸𝗿𝗮𝗶𝗻𝗶𝗮𝗻𝘀_‘𝘄𝗼𝘂𝗹𝗱_𝗳𝗶𝗴𝗵𝘁_𝘄𝗶𝘁𝗵_𝘀𝗵𝗼𝘃𝗲𝗹𝘀’_–_𝗳𝗼𝗿𝗲𝗶𝗴𝗻_𝗺𝗶𝗻𝗶𝘀𝘁𝗲𝗿

That's one of the reasons cro-magnons will die out. Stupidity down your
genes will cost you life on the planet Earth.

Go join those Neanderthals who mothered you.

[Stony Minamoto Horigoshi]

Post by Steve Banos Calogerakis
𝗨𝗸𝗿𝗮𝗶𝗻𝗶𝗮𝗻𝘀_‘𝘄𝗼𝘂𝗹𝗱_𝗳𝗶𝗴𝗵𝘁_𝘄𝗶𝘁𝗵_𝘀𝗵𝗼𝘃𝗲𝗹𝘀’_–_𝗳𝗼𝗿𝗲𝗶𝗴𝗻_𝗺𝗶𝗻𝗶𝘀𝘁𝗲𝗿

T̶h̶a̶t̶'s̶ o̶n̶e̶ o̶f̶ t̶h̶e̶ r̶e̶a̶s̶o̶n̶s̶ c̶r̶o̶-m̶a̶g̶n̶o̶n̶s̶ w̶i̶l̶l̶ d̶i̶e̶ o̶u̶t̶. S̶t̶u̶p̶i̶d̶i̶t̶y̶ d̶o̶w̶n̶ y̶o̶u̶r̶
g̶e̶n̶e̶s̶ w̶i̶l̶l̶ c̶o̶s̶t̶ y̶o̶u̶ l̶i̶f̶e̶ o̶n̶ t̶h̶e̶ p̶l̶a̶n̶e̶t̶ E̶a̶r̶t̶h̶.
G̶o̶ j̶o̶i̶n̶ t̶h̶o̶s̶e̶ N̶e̶a̶n̶d̶e̶r̶t̶h̶a̶l̶s̶ w̶h̶o̶ m̶o̶t̶h̶e̶r̶e̶d̶ y̶o̶u̶.

you suck my dick, you stoopid mazafaka, and the dick of everybody on the
planet earth. You stinking stupid mazafaka, lol. The gay smellensky is
playing piano with his penis on TV, you stinking deplorable uneducated
mazafaka. Shut the fuck up. 𝗜_𝗳𝘂𝗰𝗸_𝘆𝗼𝘂_𝗺𝗼𝘁𝗵𝗲𝗿_𝗶𝗻_𝘀𝗵𝗲_𝗮𝘀𝘀!!.

𝗡𝗔𝗧𝗢_𝗵𝗮𝘀_𝗳𝗶𝘃𝗲_𝘆𝗲𝗮𝗿𝘀_𝘁𝗼_𝗽𝗿𝗲𝗽𝗮𝗿𝗲_𝗳𝗼𝗿_𝘄𝗮𝗿_𝘄𝗶𝘁𝗵_𝗥𝘂𝘀𝘀𝗶𝗮_–_𝗺𝗲𝗺𝗯𝗲𝗿_𝘀𝘁𝗮𝘁𝗲_,𝗹𝗼𝗹
https://r%74.com/russia/590742-estonia-kallas-russian-threat/

[Chris M. Thomasson]

On Monday, January 15, 2024 at 5:05:08 AM UTC+8, Chris M. Thomasson

[...]

Post by wij
Conclusion: √2 can be exactly measure by a ruler (we can make p close to 0
to any degree we want except p≠0)
Corollary: √2(and π) is a ration number (decimal cannot be
infinitely long, no such number exists)
---------------------------------------------
Don't complain, this is your math !!!

√2 are pi are _not_ rational numbers. They can be approximated with
infinite convergents of continued fractions.

What the ruler measures is also effectively a continued fraction. The
readout
is also convergent. But the ruler cannot precisely measure irrationals
(or can it?).

Right. However, it can approximate an irrational up to a given point of
precision...

Say you want at least 7 digits of accurate precision. Continued
fractions can help out with that...