"Okay, assuming that is true, is there an intuitive way to understand that?"
I mean this quite seriously and am not being sarcastic or dismissive: Probably not. I think the general concept of "intuitive" is that there is some experiential analog to the concept in the real world, with which we've had a lot of experience and can thus "intuit" the behavior. The real world does not include infinity.
You can develop mathematical intuitions, but I don't think that's what you were saying.
In the mathematical intuition sense, it's worth pointing out the probability of any given infinite series of coin flips is zero. The all-heads or all-tails series are not special that way. While this may not be the best way to intuit it, if a metaphysical you who would live forever sat down and started flipping coins, you will never at any point be done with flipping an infinite series of coins. You could sit there until you flip any finite series of coins, but you will never flip an infinite one, even with our unrealistic stipulations of life span. From that perspective, a probability of zero of flipping an infinite number of heads should seem reasonable; there is probability zero that you will ever have flipped an infinite number of coins.
I mean this quite seriously and am not being sarcastic or dismissive: Probably not. I think the general concept of "intuitive" is that there is some experiential analog to the concept in the real world, with which we've had a lot of experience and can thus "intuit" the behavior. The real world does not include infinity.
You can develop mathematical intuitions, but I don't think that's what you were saying.
In the mathematical intuition sense, it's worth pointing out the probability of any given infinite series of coin flips is zero. The all-heads or all-tails series are not special that way. While this may not be the best way to intuit it, if a metaphysical you who would live forever sat down and started flipping coins, you will never at any point be done with flipping an infinite series of coins. You could sit there until you flip any finite series of coins, but you will never flip an infinite one, even with our unrealistic stipulations of life span. From that perspective, a probability of zero of flipping an infinite number of heads should seem reasonable; there is probability zero that you will ever have flipped an infinite number of coins.