Segment and Geographic Area Information - Schedule of Reporting Information (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Dec. 31, 2023	Sep. 30, 2023	Jun. 30, 2023	Mar. 31, 2023	Dec. 31, 2022	Sep. 30, 2022	Jun. 30, 2022	Mar. 31, 2022	Dec. 31, 2023	Dec. 31, 2022	Dec. 31, 2021
Segment Reporting Information [Line Items]
Net revenues	$ 1,613.5	$ 1,563.4	$ 1,531.2	$ 1,469.7	$ 1,430.9	$ 1,350.3	$ 1,310.8	$ 1,279.8	$ 6,177.8	$ 5,371.8	$ 4,833.8
Cost of sales									1,870.6	1,619.0	1,426.2
Selling, general and administrative expenses									2,562.0	2,228.3	2,072.0
Research, development and engineering costs									646.1	529.8	484.8
Operating profit									1,745.2	1,524.5	1,335.6
Assets:
Operating assets	1,338.9				1,163.9				1,338.9	1,163.9	1,057.6
Intangible assets, net	25,330.9				23,976.8				25,330.9	23,976.8	19,985.4
Other	1,497.7				1,840.1				1,497.7	1,840.1	788.0
Total assets	28,167.5				26,980.8				28,167.5	26,980.8	21,831.0
Capital expenditures									68.0	40.1	28.5
Capitalized software expenditures									40.0	30.2	29.7
Depreciation and other amortization									755.2	650.1	615.9
Stock-based compensation									123.5	117.8	123.0
Impairment of intangible assets									0.0	0.0	94.4
Disposal group, held-for-sale, not discontinued operations | Industrial Businesses
Assets:
Operating assets classified as held for sale											1,882.9
Application Software
Segment Reporting Information [Line Items]
Net revenues									3,186.9	2,639.5	2,366.7
Network Software
Segment Reporting Information [Line Items]
Net revenues									1,439.4	1,378.5	1,223.8
Technology Enabled Products
Segment Reporting Information [Line Items]
Net revenues									1,551.5	1,353.8	1,243.3
Operating Segments | Application Software
Segment Reporting Information [Line Items]
Net revenues									3,186.9	2,639.5	2,366.7
Operating profit									820.8	714.0	633.1
Assets:
Operating assets	730.8				624.7				730.8	624.7	576.0
Intangible assets, net	19,242.4				17,758.4				19,242.4	17,758.4	13,498.4
Other	377.7				340.2				377.7	340.2	205.8
Capital expenditures									20.1	20.7	18.0
Capitalized software expenditures									39.5	28.5	26.3
Depreciation and other amortization									563.0	455.8	418.7
Operating Segments | Network Software
Segment Reporting Information [Line Items]
Net revenues									1,439.4	1,378.5	1,223.8
Operating profit									632.4	570.6	476.8
Assets:
Operating assets	235.6				224.7				235.6	224.7	215.5
Intangible assets, net	5,005.9				5,118.5				5,005.9	5,118.5	5,364.8
Other	122.3				124.2				122.3	124.2	50.4
Capital expenditures									6.4	8.8	5.0
Capitalized software expenditures									0.5	1.7	3.4
Depreciation and other amortization									162.5	164.2	164.8
Operating Segments | Technology Enabled Products
Segment Reporting Information [Line Items]
Net revenues									1,551.5	1,353.8	1,243.3
Operating profit									518.7	449.1	415.6
Assets:
Operating assets	337.5				307.4				337.5	307.4	250.7
Intangible assets, net	1,082.6				1,099.9				1,082.6	1,099.9	1,122.2
Other	65.5				95.4				65.5	95.4	33.8
Capital expenditures									13.8	9.2	4.5
Capitalized software expenditures									0.0	0.0	0.0
Depreciation and other amortization									29.1	29.8	32.1
Corporate
Segment Reporting Information [Line Items]
Net revenues									0.0	0.0	0.0
Operating profit									(226.7)	(209.2)	(189.9)
Assets:
Operating assets	35.0				7.1				35.0	7.1	15.4
Intangible assets, net	0.0				0.0				0.0	0.0	0.0
Other	$ 932.2				$ 1,280.3				932.2	1,280.3	498.0
Capital expenditures									27.7	1.4	1.0
Capitalized software expenditures									0.0	0.0	0.0
Depreciation and other amortization									$ 0.6	$ 0.3	$ 0.3