I'm always annoyed at people who say infinity is not a number but a "concept." — Michael Lee
infinity is, by definition, uncountable. — TheMadFool
infinity is not a quantitative concept — Possibility
But a trillion trillion is uncountable, too, in that sense.
It's like there is a wilful disregard for the mathematics here. See the slide to:
infinity is not a quantitative concept
— Possibility
That's bullshit; in the technical sense - it's junk thinking indicating a lack of comprehension, wilful or otherwise. — Banno
Also, did you know that our ancestors could count only upto to 2? Look below:
Cardinal - Ordinal
1 - first
2 - second
3 - third
4 -fourth
.
.
.
n - nth
Notice that the names for ordinal numbers of the first two cardinals (1 & 2) are distinct viz. "first" and "second". All other ordinal numbers can be constructed from their respective numbers simply by adding "th". This is claimed to be be evidence of counting ability being limited to 2 and after that, 3, 4, 5,...,it was simply "many". So ancient counting looked like this: one (first), two (second), many. The many corresponds to the modern concept of infinity. As you can see, many and infinity represent a limit to quantification i.e. it spills over into the domain of quality - a concept and not a number. — TheMadFool
I'm always annoyed at people who say infinity is not a number but a "concept." For one thing, that is way too broad and says absolutely nothing; I cannot think of anything in mathematics or logic that is not a concept. I say it is a number for if it is not then one divided by infinity would not equal zero anymore than one divided by a cat is a number. Here's my definition of infinity, and for simplicity I'm only referring to positive infinity: infinity is a number, but it has a characteristic that all real numbers do not possess. Namely, it is a number that is greater than any particular real number. All the rules of arithmetic applicable to real numbers do not carry over to use of infinity. Examples: infinity plus a real number is infinity: infinity divided by infinity is not equal to one: infinity subtracted from infinity is not equal to zero. — Michael Lee
That aside, compare this "fact" of infinity with other concepts that are considered uncountable. How about love, courage, joy? These concepts are categorized as uncountable i.e. unquantifiable and fall under the category of quality. So, it doesn't seem wrong to say that infinity is not actually a quantity, a number, but rather a quality like love or courage, etc. — TheMadFool
That's bullshit; in the technical sense - it's junk thinking indicating a lack of comprehension, wilful or otherwise. — Banno
If an ancient had 5 hens...and one went missing, I suspect he would not just say..."I had many yesterday and I have many today, so no problem." — Frank Apisa
I cannot think of anything in mathematics or logic that is not a concept. — Michael Lee
infinity is a number, but it has a characteristic that all real numbers do not possess. Namely, it is a number that is greater than any particular real number. — Michael Lee
That is interesting...and I have often wondered about that kind of thing. But I suspect it is a lot more complicated than that.
If an ancient had 5 hens...and one went missing, I suspect he would not just say..."I had many yesterday and I have many today, so no problem." — Frank Apisa
But love, courage and joy are neither greater than nor less than any sort of number — Magnus Anderson
don't often say such-and-such is infinite, rather they say a process tends to infinity — jgill
Extended real number line. In mathematics, the affinely extended real number system is obtained from the real number system ℝ by adding two elements: + ∞ and − ∞ (read as positive infinity and negative infinity respectively), where the infinities are treated as actual numbers.[1] It is useful in describing the algebra on infinities and the various limiting behaviors in calculus and mathematical analysis, especially in the theory of measure and integration.[2] The affinely extended real number system is denoted R ¯ or [−∞, +∞] or ℝ ∪ {−∞, +∞}. — Wikipedia on the affinely extended real number system
It implies that if a countable first-order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ, and that no first-order theory with an infinite model can have a unique model up to isomorphism. As a consequence, first-order theories are unable to control the cardinality of their infinite models. — Wikipedia on the Löwenheim–Skolem theorem
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