Crunch on this problem gamers?!

Using the rules

1+00=00

2*00=00

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An infinite number line is drawn and placed on the number line are an infinite amount of rational and irrational numbers.

Lets suppose that if a dart was thrown at the number line it would land on the number line.

Explain why the dart will more than likely land on an irrational number than a rational number.

Hints:

Z.IR

Alright good luck!

A rational number requires all numbers after the decimal point to be recurring or fractional, whereas irrational numbers require them not to be neither. There are an infinite number of spaces after the decimal point that the numbers 0-9 can occupy, but for the purpose of this example let us limit that number to 2.

n.00, n.11, n.22, n.33, n.44, n.55 etc. are the only rational numbers in this setup as 2 decimal places serve as the limit, thus n.01 for example does not count as recurring nor to be able to adopt the m/n fraction. (In reality of course n.01 would be rational, but for a number system with 2 decimal places as the outer limit we can letthis serve as being irrational)There are 10 possible rational values between n and n+1 in total.

n.01, n.02, n.03, n.04,... etc. count as irrational numbers for the purposes of this example, as reaching the 2nd decimal place serves as the furthest the number can go, (In reality this would be infinite)and serves as reaching infinity for this case. There are 89 possible irrational values between n and n+1 in total.

As an example with up to 4 possible decimal places there would be 100 possible rational values and 9899 irrational values. With up to 8 decimal places the number of possible rational numbers would be 10000 and number of possible irrational values would be 99989999.

Stretching the number of possible decimal places up to infinity (i.e. reality) there would always be infinitely more possible irrational numbers than rational numbers.

At least... that's what I reckon the answer is...:P

Aargh. These are the sort of problems that drove Georg Cantor into a lunatic asylum. The set of rational numbers is "countably infinite", whereas the set of irrational numbers is "uncountably infinite". So the cardinality of the latter is inifinitely greater than the cardinality of the former, even though each set is infinite. Or something like that. :?

http://en.wikipedia.org/wiki/Georg_Cantor

I believe there are more irrational numbers than rational numbers

more possibilites=greater chance of being hit

Majority of you answered correctly but how are we able to determine the difference between the infinite amount of rational numbers and irrational numbers without counting. It is true that there are more irrational numbers than rational number using x=rational and 2x=irrational. What is this method called to determine the countable infinities?dracos9000

it's called i got a C in algebra 2 :'[

correct answer: i wont be tricked into during your homework for you.LoG-Sacrament

Lol this isnt homework I actually do stuff like this for fun. Odd isnt it? My real homework has to do with binary trees and sorting and searching them using the LNR,LRN, and NLR methods. The problem that this topic is about is a really small fraction of a 4000 level class called :Formal Languages, Grammar, and Automata.

Case# 2,323:

"The math nerd that never knew a woman........."

Case# 2,323:

"The math nerd that never knew a woman........."

Bobby_Oz

I am so far away from being a math nerd. My buddy is actually a math nerd and he always gets women. Maybe I should become a math nerd but Im just into computers too much. I had 1gf long long ago, but thats about it. So take a crack at the problem.

[QUOTE="Bobby_Oz"]

Case# 2,323:

"The math nerd that never knew a woman........."

dracos9000

I am so far away from being a math nerd. My buddy is actually a math nerd and he always gets women. Maybe I should become a math nerd but Im just into computers too much. I had 1gf long long ago, but thats about it. So take a crack at the problem.

Never was any good at math actually. Computers though, heh. They dont pay me for nothing :)

the correct answer is pie.....apple pieKingPeru

pi is just an irrational number and doesnt prove how its possible to know that irrational numbers are far greater than rational numbers even though both are infinite.

I know I wouldn't hit the number line and since imaginary numbers are, well, imaginary I would hit to the side and it would be imaginary.

AM I WINNAR?

[QUOTE="LoG-Sacrament"]correct answer: i wont be tricked into during your homework for you.dracos9000

Lol this isnt homework I actually do stuff like this for fun. Odd isnt it? My real homework has to do with binary trees and sorting and searching them using the LNR,LRN, and NLR methods. The problem that this topic is about is a really small fraction of a 4000 level class called :Formal Languages, Grammar, and Automata.

so somebody gave you the right answer. thats nice to know.