Acquisitions - Schedule of Business Combinations (Details) - USD ($) $ in Millions			12 Months Ended
	Sep. 06, 2018	Jul. 27, 2018	Dec. 31, 2018	Dec. 31, 2017	Dec. 31, 2016
Business Acquisition [Line Items]
Goodwill			$ 6,133.1	$ 4,560.3	$ 3,445.1
2018 Acquisitions
Business Acquisition [Line Items]
Accounts receivable			86.7
Inventories			3.9
Property, plant and equipment			7.1
Goodwill			1,601.2
Other intangible assets, primarily customer relationships, trade names and technology			1,345.8
Trade accounts payable			(9.9)
Other assets and liabilities, net			(219.7)
Previously held investment			0.0
Net cash consideration			2,815.1
2017 Acquisitions
Business Acquisition [Line Items]
Accounts receivable				103.7
Inventories				37.3
Property, plant and equipment				137.1
Goodwill				1,035.2
Other intangible assets, primarily customer relationships, trade names and technology				587.8
Trade accounts payable				(18.7)
Other assets and liabilities, net				(289.0)
Previously held investment				(36.8)
Net cash consideration				$ 1,556.6
2016 Acquisitions
Business Acquisition [Line Items]
Accounts receivable					5.2
Inventories					2.2
Property, plant and equipment					0.6
Goodwill					113.2
Other intangible assets, primarily customer relationships, trade names and technology					82.7
Trade accounts payable					(1.5)
Other assets and liabilities, net					(12.3)
Previously held investment					0.0
Net cash consideration					$ 190.1
Accruent
Business Acquisition [Line Items]
Accounts receivable	$ 54.3
Inventories	0.0
Property, plant and equipment	4.1
Goodwill	1,141.0
Other intangible assets, primarily customer relationships, trade names and technology	953.0
Trade accounts payable	(8.8)
Other assets and liabilities, net	(150.2)
Net cash consideration	$ 1,993.4
Gordian
Business Acquisition [Line Items]
Accounts receivable		$ 28.7
Inventories		0.0
Property, plant and equipment		2.6
Goodwill		428.9
Other intangible assets, primarily customer relationships, trade names and technology		386.0
Trade accounts payable		(1.0)
Other assets and liabilities, net		(67.1)
Net cash consideration		$ 778.1
Other
Business Acquisition [Line Items]
Accounts receivable			3.7
Inventories			3.9
Property, plant and equipment			0.4
Goodwill			31.3
Other intangible assets, primarily customer relationships, trade names and technology			6.8
Trade accounts payable			(0.1)
Other assets and liabilities, net			(2.4)
Net cash consideration			$ 43.6