Acquisitions and Divestitures Provisional Fair Value Estimates of Assets Acquired and Liabilities Assumed (Details) - USD ($) $ in Millions			9 Months Ended
	Sep. 06, 2018	Jul. 27, 2018	Sep. 28, 2018	Dec. 31, 2017
Business Acquisition [Line Items]
Goodwill			$ 6,743.3	$ 5,098.5
Accruent
Business Acquisition [Line Items]
Accounts receivable	$ 52.8
Property, plant and equipment	4.1
Goodwill	1,217.5
Other intangible assets, primarily customer relationships, trade names and technology	926.5
Trade accounts payable	(8.7)
Other assets and liabilities, net	(199.3)
Net cash consideration	$ 1,992.9
Gordian
Business Acquisition [Line Items]
Accounts receivable		$ 30.0
Property, plant and equipment		3.0
Goodwill		442.5
Other intangible assets, primarily customer relationships, trade names and technology		376.5
Trade accounts payable		(1.0)
Other assets and liabilities, net		(72.8)
Net cash consideration		$ 778.2
Other
Business Acquisition [Line Items]
Accounts receivable			0.0
Property, plant and equipment			0.0
Goodwill			1.8
Other intangible assets, primarily customer relationships, trade names and technology			6.8
Trade accounts payable			0.0
Other assets and liabilities, net			(0.9)
Net cash consideration			7.7
Total
Business Acquisition [Line Items]
Accounts receivable			82.8
Property, plant and equipment			7.1
Goodwill			1,661.8
Other intangible assets, primarily customer relationships, trade names and technology			1,309.8
Trade accounts payable			(9.7)
Other assets and liabilities, net			(273.0)
Net cash consideration			$ 2,778.8