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To answer your first question, I need to make explicit one of your assumptions. This can be true or false depending on what number system you are using. There are an infinite number of numbers between 1 and 2 in $$\mathbb{R}$$, the real numbers, but only a finite number (0 or 2, depending on whether you include the endpoints) in $$\mathbb{Z}$$, the integers.
To phrase your question "mathematically", you're looking for the cardinality (size) of the interval $$(1,2)$$. This cardinality is finite (0 or 2) in the integers, infinite ($$\aleph_0$$, as large as the cardinality of the integers) in the rational numbers $$\mathbb{Q}$$, and infinite ($$\mathfrak{c}$$, as large as the cardinality of the real numbers) in the real numbers. Yes, there are as many real numbers between 1 and 2 as there are in total! Isn't that crazy?