My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum


Thanks Tree5Thanks
Reply
 
LinkBack Thread Tools Display Modes
June 30th, 2017, 11:21 AM   #11
Senior Member
 
Joined: Aug 2012

Posts: 1,527
Thanks: 364

Quote:
Originally Posted by complicatemodulus View Post
..and unfortunately I'm not able to read his handy hieroglyph french.... so I've just to read what is already "translated"...
Are you saying you understand advanced algebraic geometry, category theory, schemes, and all of that? Are you making that claim? Or what exactly was your reference to Grothendieck all about?
Maschke is offline  
 
June 30th, 2017, 12:14 PM   #12
Senior Member
 
Joined: Dec 2015
From: Earth

Posts: 154
Thanks: 21

By math a number is value. but it can switch into measure ( example : physics)
idontknow is offline  
June 30th, 2017, 12:51 PM   #13
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: Southern California, USA

Posts: 1,412
Thanks: 716

Quote:
Originally Posted by idontknow View Post
By math a number is value. but it can switch into measure ( example : physics)
I would add one small bit to this. A number is an exact value, a measure will never be exact, if only due to Heisenberg.
romsek is offline  
June 30th, 2017, 01:42 PM   #14
Senior Member
 
Joined: Aug 2012

Posts: 1,527
Thanks: 364

Quote:
Originally Posted by romsek View Post
I would add one small bit to this. A number is an exact value, a measure will never be exact, if only due to Heisenberg.
Mathematical measures are exact. In fact mathematical numbers are exact, whereas no physical measurement can ever be exact.
Thanks from complicatemodulus
Maschke is offline  
June 30th, 2017, 09:44 PM   #15
Banned Camp
 
Joined: Dec 2012

Posts: 1,028
Thanks: 24

I have again to say that probably the better word I've to use is not measure, that remember the act of measuring, but "distance from".

And yes here we are playing aroud the concept of exactness (my 1/K) we use to measure the area bellow a curve we know is not like polygons and parabola derivate (and is clear that when we measure areas is usefull to use the same scale for X and Y), so can't be squared with a linear measuring instrument, but just going infimus to the integral, where the concept of "unit of measure" don't loose its signfy (we fix by our definition), but where the precision of the measure is $\infty$
complicatemodulus is offline  
June 30th, 2017, 11:04 PM   #16
Banned Camp
 
Joined: Dec 2012

Posts: 1,028
Thanks: 24

What is already known and clear is that the precision of the measure depends on the right precision of the instrument we use, so depends on witch $K$ we choose, but a bigger $K$ is not an insurance of a better measure !

See the above integration via Step Sum of a quarter of an Ellipse:

- From K=10 to K=20 the error fells lot

- from K=20 to K=50 is quasi linear but:

- K=50 gives a better result than K=60, and this is a very big problem for physics study... In this case 10time more precision is for sure better, but is not always an insurance...

complicatemodulus is offline  
July 3rd, 2017, 04:57 AM   #17
Banned Camp
 
Joined: Dec 2012

Posts: 1,028
Thanks: 24

To answer to Maschke and idontknow and some other:

Both concerning are not right since here you can see that the math is right, but you can't use the infnite precision you need to complete the Sum:

- floating point here affect the result lot due to the high number of terms and...

- if you loose a digit like 1 or 2 you loose not so much, but if you loose 8 or 9 you loose lot.

and if you keep the wrong K that get most of the high digit approximation you can have a worst result than using a littlest (not soo much) K that collect most of the lower.

Therefore you make good math, but you've always "wrong" results if you don't know exactly what you are trying to measure and witch instruments.

This problem is well known in electric circuits, for example when you've to decide if measure Volt or Ampere in a circuit: Volt comes from high resistence in the instrument (but not infinite), Ampere from low resistence in the instrument (but not zero).

I introduce the Complicate Modulus Algebra for the n-th Roots: you can play just with 2 integer value and you will not loose some digit in the computation of the Sum of several roots (in theory).

Problem is that is very slowly and usefull just for few problems involving powers.

The very good news is that after a long period of work on the "definitions" I'm finding the first theorem on the Rest.

Results are under checking...

Last edited by complicatemodulus; July 3rd, 2017 at 04:59 AM.
complicatemodulus is offline  
July 3rd, 2017, 06:21 AM   #18
Senior Member
 
Joined: Jun 2015
From: England

Posts: 662
Thanks: 187

Quote:
Originally Posted by Maschke View Post
Mathematical measures are exact. In fact mathematical numbers are exact, whereas no physical measurement can ever be exact.
Are you quite sure about that?

I measure the number of £51 notes in my pocket as exactly zero

I also measure the number of £1 coins as exactly 3.
studiot is offline  
July 3rd, 2017, 11:09 AM   #19
Senior Member
 
Joined: Aug 2012

Posts: 1,527
Thanks: 364

Quote:
Originally Posted by studiot View Post
Are you quite sure about that?

I measure the number of £51 notes in my pocket as exactly zero

I also measure the number of £1 coins as exactly 3.
I agree with your point. I think we need a philosopher of physics to explain why counting is exact but measurement isn't. My remark holds if we distinguish measurement from counting. For example the number of coins is exact but their weight can never be exact.

Last edited by Maschke; July 3rd, 2017 at 11:12 AM.
Maschke is offline  
July 3rd, 2017, 11:29 AM   #20
Senior Member
 
Joined: Jun 2015
From: England

Posts: 662
Thanks: 187

Counting is not always exact, but it is a well recognised and widely used form of measurement.

My examples were artificially constructed and arguably the count or measurement is a pure number.

But you find a Geiger counter measures counts per unit time

When you go to hospital they measure your white cell count in counts per unit volume or (microscope slide) area

Biologists, agronomists etc measure all sorts of biological counts per unit space and so on.

It could be argued that the number of strokes to complete a hole or course in golf is a measure of skill, whether it counts as just a number or not is debatable.

But all these types of measurement have one thing in common with other measurements - they are never 'exactly right' even though the answers are integrers.

But no matter how many times I count the notes in my pocket I will never find a £51 note, although I might have differing numbers of £1 coins.

Is that enough philosophy for you?

If not can I refer you to

Scientific Inference by Harold Jeffreys of @Mathematical Physics' fame.

Both are Cambridge University Press I think
Thanks from greg1313
studiot is offline  
Reply

  My Math Forum > College Math Forum > Number Theory

Tags
measure, mesaure, number



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
natural number multiple of another number if its digit sum equal to that number Shen Elementary Math 2 June 5th, 2014 07:50 AM
Zero-infinity number arrangement based on number size. Omnispark Number Theory 25 November 28th, 2013 07:01 PM
Number system - proving 9 digit number not divisible by 5 sachinrajsharma Number Theory 7 April 29th, 2013 05:49 AM
Number of Necklace/Bracelets With Fixed Number of Beads UnreasonableSin Number Theory 2 June 13th, 2010 12:03 AM
find unique n number combination in total n number jsonliu Algebra 3 May 18th, 2010 05:01 PM





Copyright © 2017 My Math Forum. All rights reserved.