smallest number used in a mathematical proof? - Page 2

cheesehead · 2006-01-05, 00:27

Quote:

Originally Posted by cheesehead

absolute magnitude

Should have been "absolute value" -- I got my hobbies mixed up.

xilman · 2006-01-05, 09:26

Quote:

Originally Posted by cheesehead

Should have been "absolute value" -- I got my hobbies mixed up.

You an astronomer too?

Sounds like we may need a new thread. Will fit in well with the M43 links crowd.

Paul

mfgoode · 2006-01-05, 09:36

Quote:

Originally Posted by cheesehead

"Smallest" refers to absolute magnitude, not algebraic value, or else ixfd64's "(excluding zero and infinitesimals)" wouldn't make sense.

Agreed cheesehead but come to think of it can a lower value than -459.67 be named that is used in Physics or mathematics?

Among lowest values Wells starts off with 0.020103040711.......equal to
199/9989 It displays the start of the Lucas sequence 2, 1, 3, 4. 7, 11.
The same sequence appears more spread out in the fraction 1999/998,999 and so on.
Mally

nibble4bits · 2006-01-08, 07:43

Magnitude by definition is the absolute value in math if I remember correctly.

1/Infinite is very close to but greater then 0? I'd guess that's why infinitely small numbers aren't allowed. Same with 0 and -infinity since one or more rules eliminate them.

The lowest number I can think of off the top of my head is the value in Farenheight of 0 degrees Kelvin which is already mentioned. This fails because it's absolute value is not small enough compared to many constants.

I'd say that 10^-120 is pretty small. This is a physics-related number that is only a very rough estimate.

mfgoode · 2006-01-11, 16:24

[QUOTE=nibble4bits]Magnitude by definition is the absolute value in math if I remember correctly.
QUOTE]

Absolute value was fomerly, and still is, called Modulus of a number but not so popular with the inclusion of modular arithmetic in the university curriculum.
The term 'Magnititude' is restricted to astronomy and is the measure of brightness of a star as compared to the brightness of a fixed star as a unit
Mally

tom11784 · 2006-01-11, 16:34

once an understanding of some linear algebra is established, it works well (in my opinion) to call it the norm of the number

nibble4bits · 2006-01-12, 09:13

What ratio of the visible mass in the universe is converted to mass every second? Even though it is an estimate, this would be a very small (or large) number.

What are the odds that a cup would reassemble itself from shards? Haha that's a good one. It has to be like a neutrino's mass - either 0 or VERY,VERY low.

mfgoode · 2006-01-28, 16:17

How about the reciprocal of M43 ?
Mally

thechickenman · 2006-01-31, 05:35

Quote:

Originally Posted by mfgoode

How about the reciprocal of M43 ?
Mally

Very small... but what proof are you going to use it in?

mfgoode · 2006-01-31, 08:58

Ha! Ha! sometimes I work backwards-first the result and then the proof! Euler did it so why not I?

Mally

nibble4bits · 2006-02-01, 02:33

I'm surprised no one has yet posted something about the late Douglas Adams or his books.

2006-01-08, 07:43	#15
nibble4bits Nov 2005 2·7·13 Posts	Magnitude by definition is the absolute value in math if I remember correctly. 1/Infinite is very close to but greater then 0? I'd guess that's why infinitely small numbers aren't allowed. Same with 0 and -infinity since one or more rules eliminate them. The lowest number I can think of off the top of my head is the value in Farenheight of 0 degrees Kelvin which is already mentioned. This fails because it's absolute value is not small enough compared to many constants. I'd say that 10^-120 is pretty small. This is a physics-related number that is only a very rough estimate. Last fiddled with by nibble4bits on 2006-01-08 at 07:45

2006-01-28, 16:17	#19
mfgoode Bronze Medalist Jan 2004 Mumbai,India 4004₈ Posts	smallest number in a mathematical proof? How about the reciprocal of M43 ? Mally

2006-01-31, 08:58	#21
mfgoode Bronze Medalist Jan 2004 Mumbai,India 2²×3³×19 Posts	smallest number in a mathematical proof? Ha! Ha! sometimes I work backwards-first the result and then the proof! Euler did it so why not I? Mally

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2006-01-11, 16:24	#16
mfgoode Bronze Medalist Jan 2004 Mumbai,India 2²×3³×19 Posts	[QUOTE=nibble4bits]Magnitude by definition is the absolute value in math if I remember correctly. QUOTE] Absolute value was fomerly, and still is, called Modulus of a number but not so popular with the inclusion of modular arithmetic in the university curriculum. The term 'Magnititude' is restricted to astronomy and is the measure of brightness of a star as compared to the brightness of a fixed star as a unit Mally

2006-01-11, 16:34	#17
tom11784 Aug 2003 Upstate NY, USA 146₁₆ Posts	once an understanding of some linear algebra is established, it works well (in my opinion) to call it the norm of the number

2006-01-12, 09:13	#18
nibble4bits Nov 2005 2·7·13 Posts	What ratio of the visible mass in the universe is converted to mass every second? Even though it is an estimate, this would be a very small (or large) number. What are the odds that a cup would reassemble itself from shards? Haha that's a good one. It has to be like a neutrino's mass - either 0 or VERY,VERY low.

2006-02-01, 02:33	#22
nibble4bits Nov 2005 2×7×13 Posts	I'm surprised no one has yet posted something about the late Douglas Adams or his books.