Revenue Impact on Financial Statements (Details) - USD ($) $ in Millions		3 Months Ended								12 Months Ended
		Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2017	Sep. 30, 2017	Jun. 30, 2017	Mar. 31, 2017	Dec. 31, 2018	Dec. 31, 2017	Dec. 31, 2016	Dec. 31, 2015
Revenue, Initial Application Period Cumulative Effect Transition [Line Items]
Lease and other revenue										$ 222.7	$ 194.6	$ 0.0
Revenues		$ 3,323.0	$ 3,143.8	$ 2,960.9	$ 3,125.2	$ 3,683.0	$ 4,140.9	$ 3,845.0	$ 3,388.0	12,552.9	15,056.9	9,199.6
Cost of lease and other revenue										143.4	137.2	0.0
Selling, general and administrative expense										1,140.6	1,060.9	572.6
Research and development expense										189.2	212.9	105.4
Impairment, restructuring and other expense (Note 17)										1,831.2	191.5	343.0
Merger transaction and integration costs (Note 2)										36.5	101.8	92.6
Costs and Expenses										13,470.5	14,091.7	8,743.6
Other income (expense), net										(323.9)	(25.9)	6.5
Income from equity affiliates (Note 9)										114.3	55.6	117.7
Income (Loss) from Continuing Operations before Interest Expense, Interest Income, Income Taxes, Noncontrolling Interests, Net										(1,127.2)	994.9	580.2
Interest Income (Expense), Nonoperating, Net										(360.9)
Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest	[1]									(1,488.1)	679.7	551.4
Provision (benefit) for income taxes										422.7	545.5	180.3
Net income (loss)		(2,246.5)	134.2	110.1	91.4	(127.5)	117.9	159.0	(15.2)	(1,910.8)	134.2	371.1
Net Income (Loss) Attributable to Noncontrolling Interest										10.8	20.9	(22.2)
Net Income (Loss) Attributable to Parent		(2,259.3)	$ 136.9	$ 105.7	$ 95.1	(153.9)	$ 121.0	$ 164.9	$ (18.7)	(1,921.6)	113.3	393.3
Cash and cash equivalents		5,540.0				6,737.4				5,540.0	6,737.4	6,269.3	$ 3,178.0
Trade receivables, net of allowances of $119.6 in 2018 and $117.4 in 2017		2,469.7				1,484.4				2,469.7	1,484.4
Contract assets		1,295.0				1,755.5				1,295.0	1,755.5
Inventories, net		1,251.2				987.0				1,251.2	987.0
Derivative Asset, Current		95.7				78.3				95.7	78.3
Income taxes receivable		284.3				337.0				284.3	337.0
Advances paid to suppliers		189.7				391.3				189.7	391.3
Other Assets, Current		655.6				1,206.2				655.6	1,206.2
Assets, Current		11,781.2				12,977.1				11,781.2	12,977.1
Investments in equity affiliates		394.5				272.5				394.5	272.5
Property, Plant and Equipment, Net		3,259.8				3,871.5				3,259.8	3,871.5
Goodwill		7,607.6				8,929.8				7,607.6	8,929.8	3,718.3	3,786.5
Intangible Assets, Net (Excluding Goodwill)		1,176.7				1,333.8				1,176.7	1,333.8
Deferred Income Tax Assets, Net		232.4				454.7				232.4	454.7
Derivative Asset, Noncurrent		18.3				94.9				18.3	94.9
Other assets		314.0				329.4				314.0	329.4
Total Assets		24,784.5				28,263.7				24,784.5	28,263.7
Long-term Debt, Current Maturities		67.4				77.1				67.4	77.1
Accounts Payable, Current		2,600.3				3,958.7				2,600.3	3,958.7
Contract liabilities		4,085.1				3,314.2				4,085.1	3,314.2
Employee-related Liabilities, Current		394.7				402.2				394.7	402.2
Derivative Liability, Current		138.4				69.0				138.4	69.0
Income taxes payable		81.9				320.3				81.9	320.3
Other Liabilities, Current		1,766.6				1,687.9				1,766.6	1,687.9
Liabilities, Current		9,134.4				9,829.4				9,134.4	9,829.4
Long-term debt		4,124.3				3,777.9				4,124.3	3,777.9
Liability, Defined Benefit Plan, Noncurrent		298.9				282.0				298.9	282.0
Derivative Liability, Noncurrent		44.9				68.1				44.9	68.1
Deferred income taxes		209.2				419.7				209.2	419.7
Other liabilities		503.4				477.2				503.4	477.2
Total liabilities		14,315.1				14,854.3				14,315.1	14,854.3
Redeemable noncontrolling interest		38.5				0.0				38.5	0.0
Ordinary shares, $1.00 par value; 618.3 shares and 525.0 shares authorized in 2018 and 2017, respectively; 450.5 shares and 465.1 shares issued and outstanding in 2018 and 2017, respectively; 14.8 and 2.1 shares canceled in 2018 and 2017, respectively		450.5				465.1				450.5	465.1
Common Stock Held in Trust		(2.4)				(4.8)				(2.4)	(4.8)
Capital in excess of par value of ordinary shares		10,197.0				10,483.3				10,197.0	10,483.3
Retained earnings		1,114.2				3,448.0				1,114.2	3,448.0
Accumulated other comprehensive loss		(1,359.7)				(1,003.7)				(1,359.7)	(1,003.7)
Stockholders' Equity Attributable to Parent		10,399.6				13,387.9				10,399.6	13,387.9
Noncontrolling interests		31.3				21.5				31.3	21.5
Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest		10,430.9				13,409.4				10,430.9	13,409.4	5,044.1	4,956.4
Liabilities and Equity		24,784.5				28,263.7				24,784.5	28,263.7
Difference between Revenue Guidance in Effect before and after Topic 606 [Member] | Accounting Standards Update 2014-09 [Member]
Revenue, Initial Application Period Cumulative Effect Transition [Line Items]
Revenues										(27.1)
Costs and Expenses										(11.8)
Income from equity affiliates (Note 9)										(8.0)
Income (Loss) from Continuing Operations before Interest Expense, Interest Income, Income Taxes, Noncontrolling Interests, Net										(23.3)
Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest										(23.3)
Provision (benefit) for income taxes										(8.9)
Net income (loss)										(14.4)
Net Income (Loss) Attributable to Parent										(14.4)
Trade receivables, net of allowances of $119.6 in 2018 and $117.4 in 2017		(1,513.4)								(1,513.4)
Contract assets		450.2								450.2
Inventories, net		16.4								16.4
Income taxes receivable		(1.2)								(1.2)
Assets, Current		(1,048.0)								(1,048.0)
Investments in equity affiliates		(8.0)								(8.0)
Deferred Income Tax Assets, Net		(0.2)								(0.2)
Total Assets		(1,056.2)								(1,056.2)
Accounts Payable, Current		17.6								17.6
Contract liabilities		(1,116.1)								(1,116.1)
Income taxes payable		2.2								2.2
Other Liabilities, Current		(39.0)								(39.0)
Liabilities, Current		(1,135.3)								(1,135.3)
Deferred income taxes		2.1								2.1
Total liabilities		(1,133.2)								(1,133.2)
Retained earnings		77.1								77.1
Stockholders' Equity Attributable to Parent		77.1								77.1
Noncontrolling interests		(0.1)								(0.1)
Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest		77.0								77.0
Liabilities and Equity		(1,056.2)								(1,056.2)
Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Revenue, Initial Application Period Cumulative Effect Transition [Line Items]
Lease and other revenue										222.7
Revenues										12,525.8
Cost of lease and other revenue										143.4
Selling, general and administrative expense										1,140.6
Research and development expense										189.2
Impairment, restructuring and other expense (Note 17)										1,831.2
Merger transaction and integration costs (Note 2)										36.5
Costs and Expenses										13,458.7
Other income (expense), net										(323.9)
Income from equity affiliates (Note 9)										106.3
Income (Loss) from Continuing Operations before Interest Expense, Interest Income, Income Taxes, Noncontrolling Interests, Net										(1,150.5)
Interest Income (Expense), Nonoperating, Net										(360.9)
Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest										(1,511.4)
Provision (benefit) for income taxes										413.8
Net income (loss)										(1,925.2)
Net Income (Loss) Attributable to Noncontrolling Interest										10.8
Net Income (Loss) Attributable to Parent										(1,936.0)
Cash and cash equivalents		5,540.0								5,540.0
Trade receivables, net of allowances of $119.6 in 2018 and $117.4 in 2017		956.3								956.3
Contract assets		1,745.2								1,745.2
Inventories, net		1,267.6								1,267.6
Derivative Asset, Current		95.7								95.7
Income taxes receivable		283.1								283.1
Advances paid to suppliers		189.7								189.7
Other Assets, Current		655.6								655.6
Assets, Current		10,733.2								10,733.2
Investments in equity affiliates		386.5								386.5
Property, Plant and Equipment, Net		3,259.8								3,259.8
Goodwill		7,607.6								7,607.6
Intangible Assets, Net (Excluding Goodwill)		1,176.7								1,176.7
Deferred Income Tax Assets, Net		232.2								232.2
Derivative Asset, Noncurrent		18.3								18.3
Other assets		314.0								314.0
Total Assets		23,728.3								23,728.3
Long-term Debt, Current Maturities		67.4								67.4
Accounts Payable, Current		2,617.9								2,617.9
Contract liabilities		2,969.0								2,969.0
Employee-related Liabilities, Current		394.7								394.7
Derivative Liability, Current		138.4								138.4
Income taxes payable		84.1								84.1
Other Liabilities, Current		1,727.6								1,727.6
Liabilities, Current		7,999.1								7,999.1
Long-term debt		4,124.3								4,124.3
Liability, Defined Benefit Plan, Noncurrent		298.9								298.9
Derivative Liability, Noncurrent		44.9								44.9
Deferred income taxes		211.3								211.3
Other liabilities		503.4								503.4
Total liabilities		13,181.9								13,181.9
Redeemable noncontrolling interest		38.5								38.5
Ordinary shares, $1.00 par value; 618.3 shares and 525.0 shares authorized in 2018 and 2017, respectively; 450.5 shares and 465.1 shares issued and outstanding in 2018 and 2017, respectively; 14.8 and 2.1 shares canceled in 2018 and 2017, respectively		450.5								450.5
Common Stock Held in Trust		(2.4)								(2.4)
Capital in excess of par value of ordinary shares		10,197.0								10,197.0
Retained earnings		1,191.3								1,191.3
Accumulated other comprehensive loss		(1,359.7)								(1,359.7)
Stockholders' Equity Attributable to Parent		10,476.7								10,476.7
Noncontrolling interests		31.2								31.2
Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest		10,507.9								10,507.9
Liabilities and Equity		23,728.3								23,728.3
Service [Member]
Revenue, Initial Application Period Cumulative Effect Transition [Line Items]
Product revenue										9,765.0	12,210.5	9,128.7
Cost of product revenue										7,895.1	9,984.0	7,585.7
Service [Member] | Difference between Revenue Guidance in Effect before and after Topic 606 [Member] | Accounting Standards Update 2014-09 [Member]
Revenue, Initial Application Period Cumulative Effect Transition [Line Items]
Product revenue										(32.0)
Cost of product revenue										(17.7)
Service [Member] | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Revenue, Initial Application Period Cumulative Effect Transition [Line Items]
Product revenue										9,733.0
Cost of product revenue										7,877.4
Product [Member]
Revenue, Initial Application Period Cumulative Effect Transition [Line Items]
Product revenue										2,565.2	2,651.8	70.9
Cost of product revenue										2,234.5	2,403.4	44.3
Product [Member] | Difference between Revenue Guidance in Effect before and after Topic 606 [Member] | Accounting Standards Update 2014-09 [Member]
Revenue, Initial Application Period Cumulative Effect Transition [Line Items]
Product revenue										4.9
Cost of product revenue										5.9
Product [Member] | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Revenue, Initial Application Period Cumulative Effect Transition [Line Items]
Product revenue										2,570.1
Cost of product revenue										2,240.4
Retained Earnings
Revenue, Initial Application Period Cumulative Effect Transition [Line Items]
Net income (loss)											113.3	393.3
Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest		$ 1,114.2				$ 3,448.0				$ 1,114.2	$ 3,448.0	$ 3,404.1	$ 3,273.4

[1] Includes amounts attributable to noncontrolling interests.