This move—this achievement—according to Paul Wilson of The Guardian, answers the ambition question for United fans.
The answer?: "Yes, the club is still ambitious and does not plan to sit back and let Manchester City have everything their own way."
And if at the end of the coming campaign, van Persie bangs in 30 goals for United and helps them reclaim "their" Premiership title—for, judging from statements one hears from that end, they now consider it their birthright—it would be said that this signing was always good business.
What's more, it'd represent strong justification for van Persie's decision to bail out of Arsenal, the apparent sinking ship. Their parsimonious ways—unwillingness to cough up £200,000 a week, van Persie's reported wages at United—has led to this loss to their immediate rival for the Premiership title.
Au Revoir, Robin van Persie. Getty Images.
This, though, is already being contested.
According to Jeremy Wilson of The Telegraph, van Persie's departure is "more damning than past departures....he has not gone to a club who are being bankrolled by a billionaire benefactor.”
This naturally implies a justification of van Persie's "vision and ambition" narrative, two commodities Arsenal apparently lacks.
Ostensibly, then, van Persie hasn't gone (or isn't going) to Manchester United for money, but for trophies, a word that no longer can be uttered in the same breath with Arsenal.
What we may note, however, is that refusing to sign for a club that offers you £130,000 a week and signing for the one that offers you £200,000 isn't a decision without some connection to money.
Nor does that decision have to be for a club "bankrolled by a benefactor" to be so. A raise is a raise no matter its source.
Come May, the "good business" would have to be acknowledged as such if United come out on top of everyone else, specifically Manchester City and Arsenal.
And although van Persie is 29 and injury prone—two factors that mitigate the "good business" narrative—if (and no matter how the coming season pans out) he goes on to have three or four productive seasons at United, at which time he'd be 33 or 34, this still would represent good business.
At 33, Andrea Pirlo taught England a lesson in class at Euro 2012. Getty Images.
This scenario is not improbable.
Consider, for example, that both Andrea Pirlo and Miroslav Klose are much older than van Persie at 33 and 34, respectively, and yet both are still firing on all cylinders and show little signs that they'll stop anytime soon.
Furthermore, "good business" will certainly be the conclusion in financial terms if Robin van Persie becomes a hit at United.
A free-scoring United could make a significant push in the lucrative Champions League, a factor that would more than make up for the reported £23 million signing fee and the additional £7,200,000 they'd have paid van Persie in wages by May.
All of this is, of course, dependent on van Persie doing well at United.
Any injury, any dip in form, and the good business wouldn't be so good. Moreover, if United misfire in the coming campaign, then the last laugh wouldn't certainly be theirs.
For Arsenal, the situation is more nuanced.
This sale has been forced by the player. The narrative, however, develops in spite of the fact.
For many, this again is yet another example of the club's lack of ambition, a situation where its inability to retain a key player stands in its way of making a serious challenge for the Premiership title, or for any trophy for that matter.
For those who accede to this narrative, no contrary opinion matters. In spite of this, though, we must consider Arsenal's disadvantaged position in face of the player's demand to leave.
Standing their ground and demanding that the player fulfill the terms of his contract (a position favored by this writer) held the possibility of still losing the player to a rival club at the end of the season, but this time for free.
Furthermore, forcing him to stay held the possibility of having around a disgruntled player, who as a result, would contribute little or nothing to Arsenal's campaign in the coming season.
(Although I have said that a good move after the coming season would be predicated upon the player maintaining his form, a fact that would likely force the player to work hard.)
His head having been turned by Manchester City, Emmanuel Adebayor's final season at Arsenal was inauspicious. This forced Arsenal to assent to his demand to leave. Nobody (perhaps) dreamed then that he'd eventually end up playing for Arsenal's rivals, Spurs. Getty Images.
In the face of this, one can hardly blame Arsenal for cashing in and hopefully moving on.
In terms of the "ambition" narrative, that hardly holds (if at all) in the face of Arsenal's decisive business in the transfer market, which has yielded three able players in Lukas Podolski, Olivier Giroud and Santi Cazorla.
The purchase of these three players negates van Persie's one indictment of the club, the ostensible reason for his desire to leave.
And as far as "good business" goes, Amy Lawrence of The Guardian has it exactly right when she says that "£20m-plus for a 29-year-old with a shaky injury history, replaced by three younger international attackers, does not sound such a terrible piece of business."
Moreover, if by any chance Arsenal were to finish above Manchester United in the coming campaign, it wouldn't sound like such a terrible piece of business, either.
In fact, this purchase puts the onus and the pressure on Manchester United to win the league.
Failure to do so wouldn't have justified what looks like a rash purchase in the light of the player's injury history, especially since it's been dubbed a show of ambition, a necessary step in the struggle to "reclaim" the title from Manchester City.
As far as pressure goes, the situation is perfect for Arsenal, since by it, they are yet again discounted as serious challengers for the Premiership title. When you are not expected to win and you do, that's a big bonus.
Alex Song. Getty Images.
Bad business can only manifest for the club if they yield to Barcelona and sell Alex Song, since in this case, there's no reason why they should.
Song was one of Arsenal's best players last season and it makes no sense to sell him, since what the club has lacked in recent years is depth.
Selling Song will be a strong manifesto on lack of ambition. I hope that there are still people at Arsenal in whom common sense still reigns supreme.