Question

Are there more numbers greater than 500, or are there more numbers less than 500?

Answer 1

More numbers greater?

Answer 2

Depends...does this include negative numbers too?

Answer 3

The same?

Answer 4

Because if that's the case, then there's neither. It's the same.

Answer 5

Hmm, really intuitive question, but I think there is both an infinite amount of numbers for both because you can go along a linegraph - infinite times and + infinite times towards positive values.

Answer 6

I would say less than. Because we can start with infinity at 500 (greater than) or go to infinity away from 500

Answer 7

so therefore, with infinity in both directions, having it start with 500 is basically infinity+500

Answer 8

@PixieDust1 yeah, but I think it's the same for both values...?:o There is always an opposite values until you can find some kind of math law of entropy here.

Answer 9

Entropy shows that in physics, energy will eventually die out, pretty morbid here- so if you could find a fact or law/equation that can prove that numbers eventually die out, you can find which side pertaining to 500 shall have more numbers or will "last" until it's time.

Answer 10

This is so TOK.

Answer 11

so you think there is the same amount of numbers above as below 500? @JackleBee

Answer 12

Yeah I think so, because if you think about, just writing domain's for a graph, you have - infinity and + infinity, in inverse equations and opposite values- so like a number line, the values extend forever. There is no end number.

Answer 13

Let
X = {x | x > 500}
Y = {y | y < 500}
We can define a function
f: X -> Y
x --> 1000 - x

f(x) = 1000 - x
Is a bijection from X to Y

Hopefully this'll cut it? ^^

Answer 14

Its the same...

Answer 15

exampli gratia: \[- \leftarrow \infty \rightarrow + \]
Yeah like terenzreignz put it in a domain and range. The values can extend forever. Until you can find a law in mathematics that does state an end to values, then sure, there might be one lenient side, but so far (or that I have heard) there are none.

Answer 16

what about fractions, are there as many fractions as we approach infty?

Answer 17

But the thing is, we can't really count infinite numbers in the traditional sense, the only way to establish "having the same number" of anything in that case is to establish a bijection, right?

f(x) = 1000 - x
seems to do the trick, whether it be from the <500 to >500, or vice versa :)

Answer 18

hmm that is a good question, there are an infinite number of fractions, because if you try to find the last fraction for lets say, between 0 and 1, you can never really reach it- it's like finding an atom from a rock- you can find it, but with maths it just gets small and smaller because of the values.

However, if you are talking about weird numbers like pi, pi I think is a value of a different sort, that isn't very natural.

Answer 19

Put in another way, with the function f(x) = 1000 - x, and accepting that it is bijective, then we can say that for every x > 500, there is a unique number 1000-x that is less than 500.

It says nothing about the nature of x, be it an integer, fraction, or irrational :D