This story is part of Apple Event, our full coverage of the latest news from Apple headquarters.
Apple on Tuesday unveiled a long list of new products and services: three new iPhones, the Apple Watch Series 5 and the launch dates and pricing for the Apple Arcade and Apple TV Plus services. Perhaps a little lost in all that, the company also wedged in a new iPad announcement, too.
In mathematics, especially in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. Preorders are more general than equivalence relations and (non-strict) partial orders, both of which are special cases of a preorder. An antisymmetric preorder is a partial order, and a symmetric preorder is an equivalence relation.
The name preorder comes from the idea that preorders (that are not partial orders) are ‘almost’ (partial) orders, but not quite; they are neither necessarily antisymmetric nor asymmetric. Because a preorder is a binary relation, the symbol ≤ can be used as the notational device for the relation. However, because they are not necessarily antisymmetric, some of the ordinary intuition associated to the symbol ≤ may not apply. On the other hand, a preorder can be used, in a straightforward fashion, to define a partial order and an equivalence relation. Doing so, however, is not always useful or worthwhile, depending on the problem domain being studied.
In words, when a ≤ b, one may say that b covers a or that a precedes b, or that b reduces to a. Occasionally, the notation ← or ≲ is used instead of ≤.
To every preorder, there corresponds a directed graph, with elements of the set corresponding to vertices, and the order relation between pairs of elements corresponding to the directed edges between vertices. The converse is not true: most directed graphs are neither reflexive nor transitive. In general, the corresponding graphs may contain cycles. A preorder that is antisymmetric no longer has cycles; it is a partial order, and corresponds to a directed acyclic graph. A preorder that is symmetric is an equivalence relation; it can be thought of as having lost the direction markers on the edges of the graph. In general, a preorder’s corresponding directed graph may have many disconnected components.
How to preorder the new 2019 10.2-inch iPad
The new seventh-generation iPad features a wider 10.2-inch screen, compared to the previous model’s 9.7 inches, and a connector for Apple’s Smart Keyboard case. Note, however, that it features the same A10 processor — which first appeared in 2016’s iPhone 7 () — as the previous 9.7-inch model.
The new iPad won’t be available in stores until Sept. 30, but Apple is already taking preorders. If you’re in the market for the most affordable full-size tablet in Apple’s line, here’s how to get your hands on one.
How to preorder the new 2019 10.2-inch iPad
7th-gen iPad pricing
Apple’s new iPad starts at $329 for the 32GB Wi-Fi model and $459 for the LTE-enabled 32GB cellular model. Bumping up storage to 128GB adds $100 to the total cost of each configuration. Education discounts get the entry-level price to $300.
Apple Event: See the iPhone 11 and Apple Watch Series 5
What’s the difference between this and the 6th-gen 9.7-inch model from 2018?
Not much. As mentioned above, the larger 10.2-inch Retina display, which replaces the 9.7-inch screen that had been in use since the first-gen iPad in 2010. The new iPad now has a dock connector for Apple’s $159 Smart Keyboard case, but both models appear to have the same A10 processor. If you’re happy with your 9.7-inch model, you should be in no hurry to upgrade.
Will the price of this one also drop to $250?
Time will tell, but that has been the de facto price of the 9.7-inch iPad since soon after it launched in March 2018. And aside from that slight bit of extra screen real estate, the new model and the previous one look to be almost interchangeable — so we wouldn’t pay more than $250 for the 32GB version of either of them. To that end, don’t buy without consulting our always-updated best iPad deals page.
Where can I get one?
Apple’s new iPad is available for preorder immediately from Apple. Preorders will begin arriving Sept. 30, when the devices become available in stores. Also, BH and Best Buy now have the new 10.2-inch models listed on their websites. You can expect to see the new iPads at all authorized Apple retailers, including Amazon, Target and Walmart, between now and Sept. 30.
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All the new products from Apple’s iPhone Event 2019
Will it have a new OS?
Yes, the new devices will come loaded with iPadOS 13, Apple’s latest update to its mobile operating system specifically tailored to iPads. Models from the old iPad Air () onward are eligible for the free update when it becomes available Sept. 30.
The best features in iOS 13 and iPadOS public beta
Apple iPad 2018 (space gray, 32GB)
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