[MrB]

As a ratio of US dollars, it could indeed approach infinity -

try dividing by 0.

[Tau Food]

Yes, that's all true in theory, but a "currency" without value is not really a "currency" because it cannot be exchanged for anything of value. Long before a currency becomes worthless, other currencies take its place. So, if the dollar loses too much value relative to other currencies and asset classes, no one will be measuring the value of gold in terms of dollars.

Beyond that, it is not necessarily safe for an investor to feel comfortable investing in gold merely because the value of gold (in dollars) is increasing. There have been periods (even recently) when both the dollar and gold have lost value in relation to other asset classes. One needs to keep an eye on all asset classes because it won't do a gold investor much good that his gold holdings are rising in dollar value if both gold and the dollar are underperforming relative to everything else. Gold and the dollar are just two of the many, many classes of assets.