In this specification, the phrase “the Number value for x” where x represents an exact nonzero real mathematical quantity (which might even be an irrational number such as π) means a Number value chosen in the following manner. Consider the set of all finite values of the Number type, with −0 removed and with two additional values added to it that are not representable in the Number type, namely 21024 (which is +1 × 253 × 2971) and −21024 (which is −1 × 253 × 2971). Choose the member of this set that is closest in value to x. If two values of the set are equally close, then the one with an even significand is chosen; for this purpose, the two extra values 21024 and −21024 are considered to have even significands. Finally, if 21024 was chosen, replace it with +∞; if −21024 was chosen, replace it with −∞; if +0 was chosen, replace it with −0 if and only if x is less than zero; any other chosen value is used unchanged. The result is the Number value for x. (This procedure corresponds exactly to the behaviour of the IEEE 754-2008 “round to nearest, ties to even” mode.)