It’s not even really a flaw. Just a property. In some sense we’ve lost the property of uniqueness of decimal representations of numbers that we had with other sets of numbers like integers. In another sense we gain alternate representations for our numbers that may be preferrable (for example 1=1.000… but also 1=0.999…).
Flaw is a bit harsh. Periodic, infinite decimals happen because the denominator is not a multiple of the prime factors of the base and thus will exist in any base.
It’s a flaw in how we decribe our numbers
It’s not even really a flaw. Just a property. In some sense we’ve lost the property of uniqueness of decimal representations of numbers that we had with other sets of numbers like integers. In another sense we gain alternate representations for our numbers that may be preferrable (for example 1=1.000… but also 1=0.999…).
Flaw is a bit harsh. Periodic, infinite decimals happen because the denominator is not a multiple of the prime factors of the base and thus will exist in any base.
Not in base infinity.
Infinity is not a number and even if you would use it as a base, you couldn’t represent anything other than infinity in a meaningful way.
Infinity^0 is indeterminate and infinity^x with x>0 is exactly infinity.