Guarantor Financial Information (Condensed Consolidating Balance Sheets) (Details) - USD ($) $ in Millions	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2017
Current assets:
Cash and cash equivalents	$ 830.9			$ 903.4	$ 1,022.5			$ 1,549.4
Accounts and notes receivable, net	2,968.9			2,679.2
Inventories	1,890.6			1,677.8
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	412.7			471.6
Due from Affiliate, Current	0.0			0.0
Total current assets	6,103.1			5,732.0
Property, plant and equipment, net	1,779.1			1,730.8
Goodwill and other intangible assets, net	10,887.2			9,594.2
Other noncurrent assets	1,537.5			857.9
Investments in and Advances to Affiliates, at Fair Value	0.0			0.0
Due from Affiliate, Noncurrent	0.0			0.0
Total assets	20,306.9			17,914.9
Current liabilities:
Current liabilities:	4,125.6			3,965.1
Short-term borrowings and current maturities of long-term debt	650.5			350.6
Short-term borrowings and current maturities of long-term debt	0.0			0.0
Total current liabilities	4,776.1			4,315.7
Long-term debt	4,921.9			3,740.7
Other noncurrent liabilities	3,329.8			2,793.7
Due to Affiliate, Noncurrent	0.0			0.0
Total liabilities	13,027.8			10,850.1
Equity:
Total equity	7,279.1	$ 7,172.9	$ 6,922.8	7,064.8	7,343.2	$ 6,823.7	$ 7,140.4	7,206.9
Total liabilities and equity	20,306.9			17,914.9
IR Ireland [Member]
Current assets:
Cash and cash equivalents	0.0			0.0	0.0			0.0
Accounts and notes receivable, net	0.0			0.0
Inventories	0.0			0.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	6.0			0.2
Due from Affiliate, Current	31.6			59.5
Total current assets	37.6			59.7
Property, plant and equipment, net	0.0			0.0
Goodwill and other intangible assets, net	0.0			0.0
Other noncurrent assets	0.0			0.0
Investments in and Advances to Affiliates, at Fair Value	10,309.5			9,308.9
Due from Affiliate, Noncurrent	0.0			0.0
Total assets	10,347.1			9,368.6
Current liabilities:
Current liabilities:	9.5			11.3
Short-term borrowings and current maturities of long-term debt	0.0			0.0
Short-term borrowings and current maturities of long-term debt	3,100.0			2,334.6
Total current liabilities	3,109.5			2,345.9
Long-term debt	0.0			0.0
Other noncurrent liabilities	0.0			0.0
Due to Affiliate, Noncurrent	0.0			0.0
Total liabilities	3,109.5			2,345.9
Equity:
Total equity	7,237.6			7,022.7
Total liabilities and equity	10,347.1			9,368.6
IR Irish Holdings [Member]
Current assets:
Cash and cash equivalents	0.1			0.1	0.0			0.0
Accounts and notes receivable, net	0.0			0.0
Inventories	0.0			0.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	0.0			0.0
Due from Affiliate, Current	0.0			0.0
Total current assets	0.1			0.1
Property, plant and equipment, net	0.0			0.0
Goodwill and other intangible assets, net	0.0			0.0
Other noncurrent assets	0.0			0.0
Investments in and Advances to Affiliates, at Fair Value	10,268.6			9,267.8
Due from Affiliate, Noncurrent	0.0			0.0
Total assets	10,268.7			9,267.9
Current liabilities:
Current liabilities:	0.0			0.0
Short-term borrowings and current maturities of long-term debt	0.0			0.0
Short-term borrowings and current maturities of long-term debt	0.0			0.0
Total current liabilities	0.0			0.0
Long-term debt	0.0			0.0
Other noncurrent liabilities	0.0			0.0
Due to Affiliate, Noncurrent	0.0			0.0
Total liabilities	0.0			0.0
Equity:
Total equity	10,268.7			9,267.9
Total liabilities and equity	10,268.7			9,267.9
IR Lux International [Member]
Current assets:
Cash and cash equivalents	0.0			0.2	40.3			0.6
Accounts and notes receivable, net	0.2			0.1
Inventories	0.0			0.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	2.4			7.8
Due from Affiliate, Current	166.9			3.9
Total current assets	169.5			12.0
Property, plant and equipment, net	0.1			0.1
Goodwill and other intangible assets, net	0.0			0.0
Other noncurrent assets	8.2			8.0
Investments in and Advances to Affiliates, at Fair Value	4,772.7			3,935.4
Due from Affiliate, Noncurrent	2,781.9			0.0
Total assets	7,732.4			3,955.5
Current liabilities:
Current liabilities:	0.0			0.1
Short-term borrowings and current maturities of long-term debt	0.0			0.0
Short-term borrowings and current maturities of long-term debt	3,019.8			132.9
Total current liabilities	3,019.8			133.0
Long-term debt	0.0			0.0
Other noncurrent liabilities	0.0			0.0
Due to Affiliate, Noncurrent	0.0			0.0
Total liabilities	3,019.8			133.0
Equity:
Total equity	4,712.6			3,822.5
Total liabilities and equity	7,732.4			3,955.5
IR Global [Member]
Current assets:
Cash and cash equivalents	0.0			0.0	0.0			0.0
Accounts and notes receivable, net	0.0			0.0
Inventories	0.0			0.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	7.6			0.0
Due from Affiliate, Current	0.0			0.0
Total current assets	7.6			0.0
Property, plant and equipment, net	0.0			0.0
Goodwill and other intangible assets, net	0.0			0.0
Other noncurrent assets	181.1			180.0
Investments in and Advances to Affiliates, at Fair Value	14,150.2			11,743.2
Due from Affiliate, Noncurrent	0.0			0.0
Total assets	14,338.9			11,923.2
Current liabilities:
Current liabilities:	47.8			41.7
Short-term borrowings and current maturities of long-term debt	0.0			0.0
Short-term borrowings and current maturities of long-term debt	3,816.4			3,518.7
Total current liabilities	3,864.2			3,560.4
Long-term debt	2,331.8			2,330.0
Other noncurrent liabilities	0.0			5.5
Due to Affiliate, Noncurrent	3,699.7			2,249.7
Total liabilities	9,895.7			8,145.6
Equity:
Total equity	4,443.2			3,777.6
Total liabilities and equity	14,338.9			11,923.2
IR New Jersey [Member]
Current assets:
Cash and cash equivalents	0.0			363.5	254.5			359.3
Accounts and notes receivable, net	166.4			183.4
Inventories	155.9			146.6
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	120.9			101.0
Due from Affiliate, Current	4,683.7			3,851.0
Total current assets	5,126.9			4,645.5
Property, plant and equipment, net	281.6			314.6
Goodwill and other intangible assets, net	425.7			432.1
Other noncurrent assets	815.5			498.1
Investments in and Advances to Affiliates, at Fair Value	11,193.5			9,923.2
Due from Affiliate, Noncurrent	0.0			0.0
Total assets	17,843.2			15,813.5
Current liabilities:
Current liabilities:	691.5			599.6
Short-term borrowings and current maturities of long-term debt	350.4			350.4
Short-term borrowings and current maturities of long-term debt	2,556.7			1,700.9
Total current liabilities	3,598.6			2,650.9
Long-term debt	312.1			319.5
Other noncurrent liabilities	1,281.9			1,100.5
Due to Affiliate, Noncurrent	0.0			0.0
Total liabilities	5,192.6			4,070.9
Equity:
Total equity	12,650.6			11,742.6
Total liabilities and equity	17,843.2			15,813.5
IR Lux Finance [Member]
Current assets:
Cash and cash equivalents	26.0			0.0	0.0			0.0
Accounts and notes receivable, net	0.0			0.0
Inventories	0.0			0.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	0.0			0.0
Due from Affiliate, Current	1,464.9			0.1
Total current assets	1,490.9			0.1
Property, plant and equipment, net	0.0			0.0
Goodwill and other intangible assets, net	0.0			0.0
Other noncurrent assets	0.0			0.0
Investments in and Advances to Affiliates, at Fair Value	1,390.1			1,264.2
Due from Affiliate, Noncurrent	0.0			0.0
Total assets	2,881.0			1,264.3
Current liabilities:
Current liabilities:	18.6			6.9
Short-term borrowings and current maturities of long-term debt	299.7			0.0
Short-term borrowings and current maturities of long-term debt	34.5			0.2
Total current liabilities	352.8			7.1
Long-term debt	2,277.9			1,091.0
Other noncurrent liabilities	0.0			0.0
Due to Affiliate, Noncurrent	0.0			0.0
Total liabilities	2,630.7			1,098.1
Equity:
Total equity	250.3			166.2
Total liabilities and equity	2,881.0			1,264.3
Other Subsidiaries [Member]
Current assets:
Cash and cash equivalents	804.8			539.6	727.7			1,189.5
Accounts and notes receivable, net	2,802.3			2,495.7
Inventories	1,734.7			1,531.2
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	275.8			363.4
Due from Affiliate, Current	6,227.7			3,838.0
Total current assets	11,845.3			8,767.9
Property, plant and equipment, net	1,497.4			1,416.1
Goodwill and other intangible assets, net	10,461.5			9,162.1
Other noncurrent assets	938.0			610.6
Investments in and Advances to Affiliates, at Fair Value	0.0			0.0
Due from Affiliate, Noncurrent	2,249.7			2,249.7
Total assets	26,991.9			22,206.4
Current liabilities:
Current liabilities:	3,358.2			3,306.3
Short-term borrowings and current maturities of long-term debt	0.4			0.2
Short-term borrowings and current maturities of long-term debt	47.4			65.2
Total current liabilities	3,406.0			3,371.7
Long-term debt	0.1			0.2
Other noncurrent liabilities	2,453.2			2,126.5
Due to Affiliate, Noncurrent	1,331.9			0.0
Total liabilities	7,191.2			5,498.4
Equity:
Total equity	19,800.7			16,708.0
Total liabilities and equity	26,991.9			22,206.4
Consolidation, Eliminations [Member]
Current assets:
Cash and cash equivalents	0.0			0.0	$ 0.0			$ 0.0
Accounts and notes receivable, net	0.0			0.0
Inventories	0.0			0.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	0.0			(0.8)
Due from Affiliate, Current	(12,574.8)			(7,752.5)
Total current assets	(12,574.8)			(7,753.3)
Property, plant and equipment, net	0.0			0.0
Goodwill and other intangible assets, net	0.0			0.0
Other noncurrent assets	(405.3)			(438.8)
Investments in and Advances to Affiliates, at Fair Value	(52,084.6)			(45,442.7)
Due from Affiliate, Noncurrent	(5,031.6)			(2,249.7)
Total assets	(70,096.3)			(55,884.5)
Current liabilities:
Current liabilities:	0.0			(0.8)
Short-term borrowings and current maturities of long-term debt	0.0			0.0
Short-term borrowings and current maturities of long-term debt	(12,574.8)			(7,752.5)
Total current liabilities	(12,574.8)			(7,753.3)
Long-term debt	0.0			0.0
Other noncurrent liabilities	(405.3)			(438.8)
Due to Affiliate, Noncurrent	(5,031.6)			(2,249.7)
Total liabilities	(18,011.7)			(10,441.8)
Equity:
Total equity	(52,084.6)			(45,442.7)
Total liabilities and equity	$ (70,096.3)			$ (55,884.5)