Can a number have infinitely many digits before the decimal point? I asked my teacher if a number can have infinitely many digits before the decimal point. He said that this isn't possible, even though there are numbers with infinitely many digits after the decimal point. I asked why and he said that if you keep adding digits to the left of a number it will eventually approach infinity which is not a number and you could no longer distinguish two numbers from one another.
Now this is the part of his reasoning I don't understand: why can we distinguish two numbers with infinitely many digits after the point but not before it? Or is there a simpler explanation for this?

What is the underlying reason for having infinitely many digits following the decimal point, but not infinitely many digits left of the decimal point? 
The underlying reason is that real numbers can have infinite precision, but only finite size. You can find larger and larger real numbers, but each of them has a finite size. You can have a real number with a gazillion digits left of the decimal point, which is a very, very, very large number, but it's still a finite number. 
To the right of the decimal point, the number of decimals is unlimited because real numbers have infinite precision. Even for rational numbers, you need an infinite number of decimals because a finite number of decimals can only represent a tiny fraction of the rational numbers. For example, 10/7 = 1.428,571,428,571,428,571... needs infinitely many decimals because if you cut of the decimals at any point the result is too small, and if you add 1 to the last digit the result is too large. 
But real numbers really need an infinite number of decimals, because after every decimal you can add any other decimal you like and you get different real numbers, and go on forever doing so. 
