Irrational numbers and infinity have made me come up with this problem: pi, for

Irrational numbers and infinity have made me come up with this problem: pi, for

Irrational numbers and infinity have made me come up with this problem: pi, for example, is an irrational number, which means that it doesn't terminate or repeat. Every new digit found in pi increases the value of the number, no matter the value of the digit (for example, 3.141 is larger than 3.14, and 3.1415 is larger than 3.141). If pi never ends, then that means that there is an infinite amount of digits that will increase the value of pi by a tiny fraction. Therefore, pi should be infinitely large. So, pi = infinity. But there is a problem: pi is between 3.13 < x <3.15. This goes far beyond pi to 1/7 and even rational numbers that don't terminate (ex. 1/3). What is the problem associated with my logic?

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