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Microsoft is now 20x bigger than IBM in terms of market cap.

the only way to settle this is to sum the market cap of both companies over their entire history while adjusting all values for inflation

keep in mind that IBM[0] is over a hundred years old, and microsoft isn't even half of that [0]

[0] wikipedia

The only way to settle this once and for all, is an arm wrestle between Arvind Krishna and Satya Nadella.

that would not settle it "once and for all"

it would merely settle "for now" becuase as soon as either of them get succeded you will have to repeat the contest

This could be a product of your own PoV & history with IBM. Not many consider IBM's legacy noteworthy, they became complacent and got beat out the market.

You can make up whatever you want, that doesn't mean it's reality. I guess Zildjian, the cymbal making company is bigger than amazon, apple, microsoft, netflix, facebook and IBM, since it was founded in 1623.

older and bigger are not synonyms. IBM is not bigger than Microsoft today. the past is irrelevant for this conversation.