Anomaly in Number System

This was a topic of hot discussion on orkut on one of the communities on Mathematics. The anomaly, more appropriately a paradox lies is the answer to a very hypothetical question.
The question is straight:
Which range contains more rational numbers?

• 0 to 1
• 1 to 10

The question being put in such a straight manner, there was not much to think about.
First of all, we have to provide some liberty to the quizzer and lets not pounce on him saying that infinity cannot be compared with infinity, rather we would say that let the number of rational numbers between 0 and 1 is x (which is very very large).
Intuitively, we can say that if we add 1 to each of these x numbers, we will get x numbers in the range 1 to 2, and adding 1 further we get another set of x numbers in range 2 to 3 and so on until we get x numbers in range 9 to 10.
By this logic, it is pretty clear that if we have x numbers in range 0 to 1 we have 9x numbers in range 1 to 10.


Now the simplicity of this problem is seriously challenged by the following counter argument.

Assume that there are y distinct rational numbers in range 1 to 10. Consider the reciprocals of all these y numbers in the range 1 to 10. There are three things that we know about these new y numbers.

1. All y are rational numbers.
2. All y are distinct (Knowing that all distinct rational numbers have distinct reciprocals).
3. All y lie between 0 and 1 (Reciprocals of numbers>1 lie between 0 and 1)

This means that the range 0 to 1 contains at least y rational numbers. (and more, eg the reciprocals of numbers greater that 10 as well)
By this logic, it is pretty clear that rational numbers lying in 0 to 1 range are far more than rational numbers lying in range 1 to 10.

Paradox or Anomaly?
How does one explain that?

"Struggle for Survival" or "Suicide for Survival"

What can be the limit of the desires of a biological species to fight extinction?
What can be the limit of a male's desire to have his female partner reject other males (of same species) only because he wants his genes to be carried forward?

If men think finding a nice partner to settle down and raise children with is tough, consider the plight of the male Australian redback spider. Instead of personality conflicts, spats over in-laws and financial worries, imagine that immediately after the first time you have sex, your partner — who is 100 to 200 times your body weight — will eat you alive.
Not the ideal honeymoon, perhaps. But redback males, who get only one mating opportunity — an uncommon occurrence in nature — have a few tricks up their (eight) sleeves.
In the process of mating, the much smaller male (Female (left) and male (right) Australian redback spiders) somersaults to place his abdomen over the female's mouthparts. In about 2 out of 3 cases, the female consumes the male while mating continues. Males who are not eaten die soon after mating.
The act of sacrificing himself allows the male two advantages over males who are not eaten. The first is that males who were eaten were able to copulate for a longer period and thus fertilise more eggs. The second is that females who had eaten a male were more likely to reject subsequent males.

Experts say, “It shows that males are really tracking the selection pressures that they’re facing in an environment — they’re aware of male density and the amount of competition they’re going to be facing. On the one hand, they want to provision themselves to survive this trip, On the other hand, they have to develop quickly so that they become sexually mature in time to mate with the virgin females before the females mate with someone else.”
The Redback spider males volunteer to suicide, only to ensure their genes are carried forward.

Source: Wikipedia http://en.wikipedia.org/wiki/Redback_spider