<p>you say 0.33333… approaches a number. Do you know the meaning of the word approaches here? Because you are saying that 0.33333… “gets closer and closer” to 1/3, and that is so not how it works. 0.33333… is one specific value, and that value can be expressed as the fraction 1/3. 0.33333… does not “fill up” a progress bar on its way to 1/3, nor does it get “closer and closer” by walking along the number line towards 1/3. It is the value 1/3, expressed in decimal notation. Tell me, do you also consider “infinity” to be a number which keeps getting bigger and bigger? Because from what you’re saying, I believe this to be your interpretation, which is wrong. “Infinity” is not a number that keeps increasing, it is a concept.</p>
<p>You must distinguish the value of the number from the way we write the number. The value of 1.3 and 0.33333… is the same. The way we write them is different.</p>