Guarantor Financial Information (Condensed Consolidating Balance Sheets) (Details) - USD ($) $ in Millions	Sep. 30, 2017	Dec. 31, 2016	Sep. 30, 2016	Dec. 31, 2015
Current assets:
Cash and cash equivalents	$ 1,259.0	$ 1,714.7	$ 1,504.6	$ 736.8
Accounts and notes receivable, net	2,468.2	2,223.0
Inventories, net	1,661.1	1,385.8
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	425.6	255.8
Due from Affiliate, Current	0.0	0.0
Total current assets	5,813.9	5,579.3
Property, plant and equipment, net	1,529.0	1,511.0
Intangible assets, net	9,592.1	9,443.5
Other noncurrent assets	787.8	863.6
Investments in and Advances to Affiliates, at Fair Value	0.0	0.0
Due from Affiliate, Noncurrent	0.0	0.0
Total assets	17,722.8	17,397.4
Current liabilities:
Current liabilities:	3,581.9	3,229.5
Short-term borrowings and current maturities of long-term debt	1,106.7	360.8
Short-term borrowings and current maturities of long-term debt	0.0	0.0
Total current liabilities	4,688.6	3,590.3
Long-term debt	2,955.9	3,709.4
Other noncurrent liabilities	3,233.9	3,379.4
Due to Affiliate, Noncurrent	0.0	0.0
Total liabilities	10,878.4	10,679.1
Equity:
Total equity	6,844.4	6,718.3	6,831.1	5,879.2
Total liabilities and equity	17,722.8	17,397.4
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, net	0.0	0.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	1.4	0.2
Due from Affiliate, Current	146.5	122.3
Total current assets	147.9	122.5
Property, plant and equipment, net	0.0	0.0
Intangible assets, net	0.0	0.0
Other noncurrent assets	0.0	0.2
Investments in and Advances to Affiliates, at Fair Value	8,840.1	7,588.1
Due from Affiliate, Noncurrent	0.0	0.0
Total assets	8,988.0	7,710.8
Current liabilities:
Current liabilities:	8.1	7.7
Short-term borrowings and current maturities of long-term debt	0.0	0.0
Short-term borrowings and current maturities of long-term debt	2,203.7	1,059.3
Total current liabilities	2,211.8	1,067.0
Long-term debt	0.0	0.0
Other noncurrent liabilities	0.0	0.0
Due to Affiliate, Noncurrent	0.0	0.0
Total liabilities	2,211.8	1,067.0
Equity:
Total equity	6,776.2	6,643.8
Total liabilities and equity	8,988.0	7,710.8
IR Irish Holdings [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, net	0.0	0.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	0.0	0.0
Due from Affiliate, Current	0.0	0.0
Total current assets	0.0	0.0
Property, plant and equipment, net	0.0	0.0
Intangible assets, net	0.0	0.0
Other noncurrent assets	0.0	0.0
Investments in and Advances to Affiliates, at Fair Value	1,633.9	1,500.4
Due from Affiliate, Noncurrent	12,560.2	12,560.2
Total assets	14,194.1	14,060.6
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	14,194.1	14,060.6
Total liabilities and equity	14,194.1	14,060.6
IR Lux International [Member]
Current assets:
Cash and cash equivalents	0.0	0.0	0.1	0.0
Accounts and notes receivable, net	0.0	0.0
Inventories, net	0.0	0.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	5.7	5.3
Due from Affiliate, Current	1.8	5.6
Total current assets	7.5	10.9
Property, plant and equipment, net	0.0	0.0
Intangible assets, net	0.0	0.0
Other noncurrent assets	0.0	0.0
Investments in and Advances to Affiliates, at Fair Value	2,963.7	3,267.1
Due from Affiliate, Noncurrent	0.0	0.0
Total assets	2,971.2	3,278.0
Current liabilities:
Current liabilities:	0.2	0.2
Short-term borrowings and current maturities of long-term debt	0.0	0.0
Short-term borrowings and current maturities of long-term debt	1,987.5	3,400.1
Total current liabilities	1,987.7	3,400.3
Long-term debt	0.0	0.0
Other noncurrent liabilities	0.0	0.0
Due to Affiliate, Noncurrent	6,376.3	6,376.3
Total liabilities	8,364.0	9,776.6
Equity:
Total equity	(5,392.8)	(6,498.6)
Total liabilities and equity	2,971.2	3,278.0
IR Global [Member]
Current assets:
Cash and cash equivalents	0.2	0.0	0.0	11.4
Accounts and notes receivable, net	0.0	0.0
Inventories, net	0.0	0.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	8.1	0.7
Due from Affiliate, Current	0.0	271.6
Total current assets	8.3	272.3
Property, plant and equipment, net	0.0	0.0
Intangible assets, net	0.0	0.0
Other noncurrent assets	276.8	262.4
Investments in and Advances to Affiliates, at Fair Value	8,060.9	7,270.2
Due from Affiliate, Noncurrent	0.0	0.0
Total assets	8,346.0	7,804.9
Current liabilities:
Current liabilities:	56.0	36.3
Short-term borrowings and current maturities of long-term debt	749.4	0.0
Short-term borrowings and current maturities of long-term debt	1,021.6	1,068.2
Total current liabilities	1,827.0	1,104.5
Long-term debt	1,539.3	2,286.3
Other noncurrent liabilities	21.2	18.2
Due to Affiliate, Noncurrent	1,817.2	1,817.2
Total liabilities	5,204.7	5,226.2
Equity:
Total equity	3,141.3	2,578.7
Total liabilities and equity	8,346.0	7,804.9
IR New Jersey [Member]
Current assets:
Cash and cash equivalents	464.8	634.6	541.3	0.0
Accounts and notes receivable, net	149.2	171.0
Inventories, net	184.1	165.3
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	76.4	69.4
Due from Affiliate, Current	895.3	220.5
Total current assets	1,769.8	1,260.8
Property, plant and equipment, net	310.1	445.9
Intangible assets, net	412.4	414.7
Other noncurrent assets	680.8	676.3
Investments in and Advances to Affiliates, at Fair Value	16,440.1	15,273.4
Due from Affiliate, Noncurrent	0.0	0.0
Total assets	19,613.2	18,071.1
Current liabilities:
Current liabilities:	559.1	525.1
Short-term borrowings and current maturities of long-term debt	350.4	350.4
Short-term borrowings and current maturities of long-term debt	8,415.1	6,285.6
Total current liabilities	9,324.6	7,161.1
Long-term debt	326.7	334.2
Other noncurrent liabilities	1,210.7	1,280.8
Due to Affiliate, Noncurrent	700.0	2,034.6
Total liabilities	11,562.0	10,810.7
Equity:
Total equity	8,051.2	7,260.4
Total liabilities and equity	19,613.2	18,071.1
IR Lux Finance [Member]
Current assets:
Cash and cash equivalents	0.0	0.0	0.1	0.1
Accounts and notes receivable, net	0.0	0.0
Inventories, net	0.0	0.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	0.0	0.0
Due from Affiliate, Current	0.0	0.0
Total current assets	0.0	0.0
Property, plant and equipment, net	0.0	0.0
Intangible assets, net	0.0	0.0
Other noncurrent assets	0.0	0.0
Investments in and Advances to Affiliates, at Fair Value	1,002.3	1,090.4
Due from Affiliate, Noncurrent	0.0	0.0
Total assets	1,002.3	1,090.4
Current liabilities:
Current liabilities:	16.8	7.0
Short-term borrowings and current maturities of long-term debt	0.0	0.0
Short-term borrowings and current maturities of long-term debt	501.2	486.9
Total current liabilities	518.0	493.9
Long-term debt	1,089.4	1,088.3
Other noncurrent liabilities	0.0	0.0
Due to Affiliate, Noncurrent	0.0	0.0
Total liabilities	1,607.4	1,582.2
Equity:
Total equity	(605.1)	(491.8)
Total liabilities and equity	1,002.3	1,090.4
Other Subsidiaries [Member]
Current assets:
Cash and cash equivalents	794.0	1,080.1	963.1	725.3
Accounts and notes receivable, net	2,319.0	2,052.0
Inventories, net	1,477.0	1,220.5
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	334.5	189.3
Due from Affiliate, Current	13,138.3	11,747.9
Total current assets	18,062.8	16,289.8
Property, plant and equipment, net	1,218.9	1,065.1
Intangible assets, net	9,179.7	9,028.8
Other noncurrent assets	526.5	580.1
Investments in and Advances to Affiliates, at Fair Value	0.0	0.0
Due from Affiliate, Noncurrent	2,517.2	3,851.8
Total assets	31,505.1	30,815.6
Current liabilities:
Current liabilities:	2,942.2	2,662.3
Short-term borrowings and current maturities of long-term debt	6.9	10.4
Short-term borrowings and current maturities of long-term debt	52.8	67.8
Total current liabilities	3,001.9	2,740.5
Long-term debt	0.5	0.6
Other noncurrent liabilities	2,698.3	2,735.8
Due to Affiliate, Noncurrent	6,183.9	6,183.9
Total liabilities	11,884.6	11,660.8
Equity:
Total equity	19,620.5	19,154.8
Total liabilities and equity	31,505.1	30,815.6
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, net	0.0	0.0
OtherAssetsCurrentAndDeferredTaxesAndTaxReceivable	(0.5)	(9.1)
Due from Affiliate, Current	(14,181.9)	(12,367.9)
Total current assets	(14,182.4)	(12,377.0)
Property, plant and equipment, net	0.0	0.0
Intangible assets, net	0.0	0.0
Other noncurrent assets	(696.3)	(655.4)
Investments in and Advances to Affiliates, at Fair Value	(38,941.0)	(35,989.6)
Due from Affiliate, Noncurrent	(15,077.4)	(16,412.0)
Total assets	(68,897.1)	(65,434.0)
Current liabilities:
Current liabilities:	(0.5)	(9.1)
Short-term borrowings and current maturities of long-term debt	0.0	0.0
Short-term borrowings and current maturities of long-term debt	(14,181.9)	(12,367.9)
Total current liabilities	(14,182.4)	(12,377.0)
Long-term debt	0.0	0.0
Other noncurrent liabilities	(696.3)	(655.4)
Due to Affiliate, Noncurrent	(15,077.4)	(16,412.0)
Total liabilities	(29,956.1)	(29,444.4)
Equity:
Total equity	(38,941.0)	(35,989.6)
Total liabilities and equity	$ (68,897.1)	$ (65,434.0)