Infinity is not a number like any other real number; you can call it undefined. As such, you cannot think of infinity as a finite count; i.e. it is not a single number. So, in your two sets, both of the sets have infinite number of elements.

Even our Yajurveda has a definition for infinity and this might clarify further: If you remove a part from infinity or add a part to the infinity, what you will get is still infinity (i.e. not infinity+part). Infinity can thus be taken as a concept here.

If that's not clear, one last try, my own way:
When you divide a number, say, 100 by 50 you will get two parts.
Now, divide 100 by 10 and you will get 10 parts. 100 is your numerator and 10 is the denominator. As you keep on dicreasing the denominator, you will get more and more parts (quotient).When 100 is divided by 1, you will get even more parts (100 parts). Divide 100 by 0.1 and now you get 1000 parts; divide 100 by 0.01 you get 10000 parts and so on.
Now, imagine you keep on dividing 100 by 0.00....0001; you will get a really big number.
0 is less than 0.000....001 so when you divide 100 by 0, you will get a number so big, you cannot even divide. But let's think about what we've done here, dividing 100 by 50 means, dividing 100 into 50 parts. What does dividing 100 by 0 mean? Dividing 100 into 0 parts..that doesn't make sense in conventional form, right? That's your infinity; undefined.