Largest number
There is no largest number. However, there is nothing contradictory about a number that is larger than any particular number you can define using ordinary mathematics. Simply add a symbol for such a number to math and add for each closed term of ordinary mathematics (that is, mathematics not containing that primitive symbol) an axiom that the number defined by the symbol is larger than the number defined by the term if the term defines a number. Roughly speaking, a number is large if for any number that you can define in ordinary mathematics, it is provable that it is larger than that number (but of course it is not provable that the number is larger than all numbers, because then, for example, it would be larger than its successor). You don't get a contradictory theory, because if you did you would have a finite proof of a contradiction, and you could always interpret the large number you introduce so large that any new axiom you introduce in said proof becomes true when interpreted.
The real use of this or analogous constructions is what you get when you, say, take the reciprocal of the number you introduce. You get a number smaller in magnitude than any "standard" positive number. Such a number is called a "small" number, a useful concept in Calculus or analysis, for instance. Thus, in math one can say that for any particular (i.e., definable in ordinary math) f and a, f continuous at a means that if a is near b, f(a) is near f(b), where "a near b" means that the absolute value of a - b is small. Such matters are studied (using slightly different approaches) in non-standard analysis, or better yet, Internal Set Theory (the latter probably the more elegant and properly generalized). Probably, there is a kind of usage concerning "any" and "all", etc., that needs to be more generally recognized before these approaches really becomes sufficiently natural to be at once useful and unambiguous in mathematical discourse.
truth
IN A SENSE, 1 is the largest and only number there is. All other"numbers" are merely accumulations of 1s
JL... that works for integrs. How about Real numbers?
truth
Sealpoet, I'm glad it works for something. I can't answer your question for fear of a major humiliation. Despite my years of graduate training I remain a mathematical illiterate.
Now that I think about it, the largest number could be an imaginary number....
I guess it depends if the universe is finite or not. If it is finite, if there is/was an end and beginning, would that also apply to numbers,
. A largest and a smallest?
I don't believe there can be such a thing. Numbers were invented to attempt to measure things, many of which we still do not comprehend. Therefore, numbers are both finite and infinite, and mathematics an intriguing but inexact science.
truth
If I had to take a guess, I would guess that numbers have no objective reality; they are our constructions, tools for thinking about what we see as objective physical reality.
Actual numbers like words have object reality when there put out there although they're meaningless or void of meaning in and of them self,
..but then there probably is no in-and-of-them-self.
Could the largest number be an irrational number?
Write an irrational number?
8
0
The starting prime is 43,804,034,644,029,893,325,717,710,709,965,599,930,101,479,007,432,825,862,362,446,333,961,919,524,977,985,103,251,510,661, with each successive prime 210 larger.
all numbers are the same size, as each number is defined in its meaning by all other numbers which it is not; and are then present by default.
they usually same something like "size doesn't really matter" but I don't think they are sincere.
Psst...to all you natural selection buffs...if size didn't matter, why do human males statistically have the largest penises of all the primate species? Makes ya think....
cavfancier wrote:Psst...to all you natural selection buffs...if size didn't matter, why do human males statistically have the largest penises of all the primate species? Makes ya think....
can you get some facts on that?
an I don't think looking in er own shorts counts! way to subjective
truth
Cav, if that's so, why is there so large a market (at least on the internet) for penis growth pills and devices. I wish we could make contact them and ask for penis reducers. Just kidding, of course.
Twyvel, don't you mean to place the 8 on its side? (the symbol for infinity)
