Therefore when F = 0, you are further away. But r1 → ∞, so r2 must tend to a greater infinity.

Consider what you are saying;

r1 → ∞, but it could never reach infinity. However far it goes it is infinitely far from infinity.

r2 → ∞, but it could never reach infinity. However far it goes it is infinitely far from infinity.

In both cases you are infinitely far from infinity before you start, and when you finish. Other than as a mathematical necessity, how does one infinity differ from the other?

Your reasoning is impeccable, as long as you consider infinity as a finite distance, which, manifestly it is not.

In this, and all of your examples, you are using mathematical infinities; I have no problem with that, and your arguments make perfect sense, as long as one remembers that mathematical infinities are approximations.

Interesting that you should mention Welsh words that have no need for vowels. Let’s take a simple example, the word “pwll”; a Welshman looks at that and says: “lets call w a vowel”. Now pwll has a vowel in it.

Ar hyn sail, tybed os bob siaradwyr Cymraeg yn wyddonwyr. [

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