111–120 of 398 posts
This is also how we get to the notion of infinities larger than other infinities.
Earlier quoted context omitted.
Some do, yes. If they have an aptitude for basic sums then pointing out that 3 x 3 is the same as 3 + 3 + 3 sets them down the right path ...
I think you need to spend more time around six year olds ;)
I want to know if there are more decimal numbers between 0 and 1 than there are integers between 0 and infinity.
There are, and it turns out that this is a significant mathematical concept. The integers between 0 and infinity are defined as "countably infinite". Other infinities are considered countably infinite, or the "same" infinity, if and only if you can arrange it in a list such that each item in the list pairs to an integer in our 0 to infinity list. So the set of even numbers is countably infinite because for every i th…
The way I parse "decimal number" in this context is a number expressible as a (finite?) string of decimal numerals. Those numbers are not reals, they are rationals.
Infinity is not a number, it's the absence of a limit.
In JavaScript we're spoiled by having both. There's Number.NEGATIVE_INFINITY and Number.POSITIVE_INFINITY.
npm install is-odd
const isOdd = require('is-odd');
console.log(isOdd(∞));Earlier quoted context omitted.
No it isn't. If you ask a child what comes after infinity, "Infinity + 1" is pretty much the default answer. Any kid who knows multiplication knows "Infinity + Infinity" is the same as "Infinity Times Two". The answer of "Infinity TIMES Infinity" is also popular for kids to say when they know a number bigger than their friend (who just proclaimed infinity is the largest number).
> Any kid who knows multiplication knows "Infinity + Infinity" is the same as "Infinity Times Two". Or is it "Two Times Infinity"? (Hint: It isn't, because "Two Times Infinity" = "Infinity", while "Infinity Times Two" = "Infinity + Infinity". Not sure every kid knows that.)
Earlier quoted context omitted.
> Any kid who knows multiplication knows "Infinity + Infinity" is the same as "Infinity Times Two". Or is it "Two Times Infinity"? (Hint: It isn't, because "Two Times Infinity" = "Infinity", while "Infinity Times Two" = "Infinity + Infinity". Not sure every kid knows that.)
This seems to disregard the commutative property of multiplication
To explain to a six-year-old I would start by telling them that there are many different kinds of infinity, not just one. Some infinities are odd, others are even, and others are neither. It matters whether you are asking "how many" (cardinals) or "in what position" (ordinals). For regular finite numbers, cardinals and ordinals are (more or less) the same, but for infinities they behave differently. Then, if they wan…
For a child, I think the simplest kind of infinity to explain is the cardinality of integers—"how many numbers there are."
> It is easy to prove from this definition by transfinite recursion that the ordinals come in an alternating even/odd pattern, and that every limit ordinal (and hence every infinite cardinal) is even.
Sure, if we use the natural numbers and start at 1, then we can group:
[1, 2], [3, 4], [5, 6], ...
But we could also just as easily group:
1, [2, 3], [4, 5], [6, 7], ...
It's the same if we try to split into two equal subsets, because we can split into:
[1, 3, 5, ...]
[2, 4, 6, ...]
1
[2, 4, 6, ...]
[3, 5, 7, ...]
So I'm missing the reason for why the second versions aren't just as valid.
(Of course, I'm more inclined to agree with many commenters here that it's just a category error, and asking whether infinity is even/odd is as useful as asking whether democracy is blonde or brunette.)
> Infinity is not a number, odd or even, but rather a concept or a mathematical idea that represents an unbounded or limitless quantity. Infinity is not a real number that can be used in ordinary arithmetic operations, but it is used to describe a quantity that is larger than any finite number. Therefore, the concept of odd or even does not apply to infinity.