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Other Intangible Assets, net and Goodwill - Narrative (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Goodwill [Line Items]
Amortization of intangible assets	$ 161.1	$ 128.1	$ 492.7	$ 383.4
Goodwill impairment charge	4,407.9		4,407.9
Academia & Government
Goodwill [Line Items]
Goodwill impairment charge	1,745.8		1,745.8
IP Segment
Goodwill [Line Items]
Goodwill impairment charge			$ 2,662.1
IP Segment | IP Management
Goodwill [Line Items]
Goodwill impairment charge	2,569.1
IP Segment | Patent
Goodwill [Line Items]
Goodwill impairment charge	$ 93.0

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- Definition

The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method.

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Amount of divestiture of an asset representing future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized.

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