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Shareholders' equity - Purchase of Equity Securities (Details) - EUR (€) € / shares in Units, € in Millions | 1 Months Ended | 12 Months Ended | 13 Months Ended | 14 Months Ended | 15 Months Ended | 16 Months Ended | 17 Months Ended | 18 Months Ended | 19 Months Ended | 20 Months Ended | 21 Months Ended | 22 Months Ended | 23 Months Ended | 35 Months Ended | 38 Months Ended
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Nov. 30, 2022 | Oct. 31, 2022 | Sep. 30, 2022 | Aug. 31, 2022 | Jul. 31, 2022 | Jun. 30, 2022 | May 30, 2022 | Apr. 30, 2022 | Mar. 31, 2022 | Feb. 28, 2022 | Jan. 31, 2022 | Dec. 31, 2022 | Jan. 31, 2022 | Dec. 31, 2021 | Dec. 31, 2020 | Dec. 23, 2022 | Feb. 28, 2022 | Mar. 31, 2022 | Apr. 30, 2022 | May 31, 2022 | Jun. 30, 2022 | Jul. 31, 2022 | Aug. 31, 2022 | Sep. 30, 2022 | Oct. 31, 2022 | Nov. 30, 2022 | Dec. 31, 2022 | Dec. 31, 2022 | Dec. 31, 2025
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Total number of shares purchased (in shares) | 152,323 | 237,399 | 907,391 | 673,412 | 666,112 | 717,092 | 675,117 | 808,095 | 1,241,647 | 1,150,011 | 1,107,187 | 8,538,787 | 1,107,187 | 14,358,838 |  | 203,001 | 2,257,198 | 3,498,845 | 4,306,940 | 4,982,057 | 5,699,149 | 6,365,261 | 7,038,673 | 7,946,064 | 8,183,463 | 8,335,786 | 8,538,787 |  |
Treasury stock, repurchased |  |  |  |  |  |  |  |  |  |  |  | € 4,639.7 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Purchase of treasury shares |  |  |  |  |  |  |  |  |  |  |  | € 4,639.7 |  | € 8,560.3 | € 1,207.5 |  |  |  |  |  |  |  |  |  |  |  |  |  |
Treasury shares, cancellation process started during the year (in shares) |  |  |  |  |  |  |  |  |  |  |  | 3,337,825 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Cancelled shares (in shares) |  |  |  |  |  |  |  |  |  |  |  |  |  | 13,023,016 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Average price paid per share (Euro per share) | € 568.91 | € 431.23 | € 466.94 | € 541.36 | € 467.26 | € 488.27 | € 522.70 | € 573.12 | € 575.99 | € 572.80 | € 630.21 | € 543.37 |  |  |  | € 558.33 |  |  |  |  |  |  |  |  |  |  |  |  |
Maximum value of shares that may yet be purchased (€ millions) | € 11,913.3 | € 0.0 | € 102.4 | € 526.1 | € 890.6 | € 1,201.9 | € 1,552.0 | € 1,904.9 | € 2,368.0 | € 3,083.2 | € 3,741.9 |  |  |  |  | € 11,800.0 |  |  |  |  |  |  |  |  |  |  |  |  |
New share buyback program |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Total number of shares purchased (in shares) |  |  |  |  |  |  |  |  |  |  |  | 355,324 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Treasury stock, repurchased |  |  |  |  |  |  |  |  |  |  |  | € 200.0 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Share buyback program 2020-2022 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Expected total value of purchased shares |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | € 9,000.0 |
Cancelled shares (in shares) |  |  |  |  |  |  |  |  |  |  |  | 3,337,825 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Forecast [Member] | Share Buyback Program 2022-2025 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Expected total value of purchased shares |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | € 12,000.0
Expected shares to be purchased for award (in shares) |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | € 2.0

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