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Fri 9 Feb, 2007 09:44 am
Is infinity a sub-unit of another number? (Example: 1 is a sub-unit of 2) :wink:
I thought that "infinities" could be of different "sizes" so in that sense the "infinity of rational numbers between 1 and 2" could be thought of as a "sub-unit" of "the infinitity of positive integers". However I claim no knowledge of a rigorous definition of the term "sub-unit".
What do you mean when you say that "1 is a "sub-unit of 2?" Do you mean "less than?"
infinity is not a real thing, it was made up by mathematicians as a convenience. by definition, there is no number larger than infinity. although, if a->inf and b->inf, we can still sometimes say that a > b because a goes at a faster rate than b...but when looking at inf itself, the equality operators are undefined for good reason.
stuh505 wrote:infinity is not a real thing, it was made up by mathematicians as a convenience. by definition, there is no number larger than infinity. although, if a->inf and b->inf, we can still sometimes say that a > b because a goes at a faster rate than b...but when looking at inf itself, the equality operators are undefined for good reason.
It's not a number, but I'm not sure it isn't real. Are negative numbers real? How about imaginary and complex numbers? Matrices?
Brandon,
knstech was essentially suggesting that there existed some number that we might "discover" that infinity was smaller than. I was trying to explain that, since we dont "discover" numbers but rather define them to be what we want, and since we have defined infinity such that there is no larger number, there is no chance of what he suggested being true.
stuh505 wrote:infinity is not a real thing,
It is in the sense of a non-random repeating number such as 1.666......
This can, for all intents and purposes, be rounded up..... like little doogies.
Git along little doogies!
Re: Infinity?
knstech wrote:Is infinity a sub-unit of another number? (Example: 1 is a sub-unit of 2) :wink:
Defne what you mean by you use of the word infinity.
Noun 1. subunit - a monetary unit that is valued at a fraction (usually one hundredth) of the basic monetary unit
What definition of sub-unit are you using?
Infinity is a concept of an un-ending number - not a number in itself. It can not generally be used in nummerical calculations with numbers in a field. It can be used in limit theory, differential calculus or non eucledian geometry - to name a few applicable fields of legitimate mathematical use. Within these fields (especially limits) it can be "sized" (a small inifinity, a exponential infinity etc - generally determined as the relative growth rate of series that heads out starting from zero with no limit). So the sum of all positive numbers may be classed a "small, linear" inifinity (considered as branching out from zero), whilst the sum of the factorials of all positive integers (by relative comparision) is a rather large, exponential infinity.
General rule for maths below 2nd year Uni - don't mix numbers and infinities unless doing limit theory or doing the curls of vector forces around an anomaly in a 3d space...
Brandon9000 wrote:stuh505 wrote:infinity is not a real thing, it was made up by mathematicians as a convenience. by definition, there is no number larger than infinity. although, if a->inf and b->inf, we can still sometimes say that a > b because a goes at a faster rate than b...but when looking at inf itself, the equality operators are undefined for good reason.
It's not a number, but I'm not sure it isn't real. Are negative numbers real?
Of course negative numbers are "real". Consider this example:
There are 5 people in a room. Seven people leave. How many people have to enter the room for it to be empty?
ebrown_p wrote:Of course negative numbers are "real". Consider this example:
There are 5 people in a room. Seven people leave. How many people have to enter the room for it to be empty?
The word "entering" means coming INTO the room. No amount of things can be put INTO the room to make it empty.
ebrown_p wrote:Brandon9000 wrote:stuh505 wrote:infinity is not a real thing, it was made up by mathematicians as a convenience. by definition, there is no number larger than infinity. although, if a->inf and b->inf, we can still sometimes say that a > b because a goes at a faster rate than b...but when looking at inf itself, the equality operators are undefined for good reason.
It's not a number, but I'm not sure it isn't real. Are negative numbers real?
Of course negative numbers are "real". Consider this example:
There are 5 people in a room. Seven people leave. How many people have to enter the room for it to be empty?
I know. My point was to suggest to him that infinity, and many other things besides the natural numbers are real, not to actually suggest that negative numbers are not.
Stuh,
Thats the point (which is somewhat amusing to me at least).
This problem has a perfectly correct mathematical solution; 5 - 7 = -2 people are in the room after the first part of the problem
Obviously, an empty room has zero people -- so to get an empty room requires +2 people which is also a perfectly fine solution.
But is raises the question-- is -2 people a "real" number of people to have in a room?
If this doesn't amuse you, just let it go.
In the absence of a a definition of the term "sub-unit", surely all we can say is that "real" in mathematics is a technical term which distinguishes the "real numbers" (horizontal number line) from the "imaginary numbers" (vertical number line). and in this technical sense a negative integer is "real".
However this is not a concept of "reality" which can be extended to "infinity" or "infinities". Here we are dealng with philosophical and operational notions about the process of "counting". There is an interesting book called "Infinity and the Mind" by Rucker which goes into these concepts in depth.
Hi-yah fresco,
I (finally) responded to your post about Spinoza's proposed proof that god doesn't exist as per Session 5 Speaker 2!
http://www.able2know.com/forums/viewtopic.php?t=90688&start=610
Thanks....have responded thereto.
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