I want to know if there are more decimal numbers between 0 and 1 than there are integers between 0 and infinity.
If you consider non-repeating, non-terminal decimals (like say pi/4) then yes. Otherwise no.
Is infinity an odd or even number? (2011)
91–100 of 398 posts
Re: Is infinity an odd or even number? (2011)
#92Earlier quoted context omitted.
I don't usually use that term, but I take it to mean "number you (may, and, if not using e.g. fractions, must) write using a decimal point" because that seems to always be what people intend by it. Everybody experienced writing irrational numbers using decimal notation in school, so those definitely count.
> Everybody experienced writing irrational numbers using decimal notation in school, To be pedantic, we experienced writing approximations of these numbers in decimal arithmetic.
It’s not just pedantic! It completely changes the answer to the question.
Re: Is infinity an odd or even number? (2011)
#93i think making the odd/even distinction is a mistake. It makes people say things like "2 is the only even prime" as if that's somehow different than "3 is the only prime evenly divisible by 3".
Even is a quality of division when the remainder is 0; even is a quality of making a rectangle with discrete integral sides.
Re: Is infinity an odd or even number? (2011)
#94Earlier quoted context omitted.
Depends what you mean by decimal. Decimal is a system of notation, does it count as a decimal number if it cannot be written in decimal notation (in finite time)? if not then they are equal, if yes then there are more decimal numbers between 0 and 1 than integers.
I don't usually use that term, but I take it to mean "number you (may, and, if not using e.g. fractions, must) write using a decimal point" because that seems to always be what people intend by it. Everybody experienced writing irrational numbers using decimal notation in school, so those definitely count.
Nobody ever finished writing an irrational number in school.
Re: Is infinity an odd or even number? (2011)
#95To 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."
Re: Is infinity an odd or even number? (2011)
#96I want to know if there are more decimal numbers between 0 and 1 than there are integers between 0 and infinity.
Assuming sqrt(2)/2 is one of the elements of your set between 0 and 1, there are! See https://en.m.wikipedia.org/wiki/Countable_set
Sqrt(2)/2 can not be written as a decimal number.
A decimal number is a rational whose denominator is an integer power of 10.
Re: Is infinity an odd or even number? (2011)
#97Re: Is infinity an odd or even number? (2011)
#98Infinity is not a number, it's the absence of a limit.
NaN
Re: Is infinity an odd or even number? (2011)
#99Earlier 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 had it explained at a very early age as "three lots of three", and to imagine it like three boxes of three ice-creams. Treating the multiplication symbol as one would to indicate quantity in a list, thus calculating how many ice-creams there are.
Found the Brit! As an American I’d never heard the “lots of __” phrasing until I watched Numberblocks (a British show) with my kid…
Re: Is infinity an odd or even number? (2011)
#100Is infinity an integer?
Nope. Nor a rational number. Nor a real number. Nor...