jakef

Who would buy this thing? The phone doesn't look to be anything special, the name makes it sound low-end, there's zero brand recognition. The magnetic wireless accessory thing is irrelevant to vast majority of consumers, especially since Bluetooth has already solved that problem and works with any device.

I can't imagine a scenario where someone is looking to buy a phone in the ~$700 range and chooses this.

This article is talking about the cardinality of two very specific sets. Before, many believed that t > p, but many believed that this was not provable in ZFC. Both sets contain only sets of integers, so their cardinality is bounded above by the cardinality of the real numbers (the continuum). Some people believed that this result was related to the Continuum hypothesis, and so was only provable one way or the other if you assume the CH or its negative.

As it turns out, both sets have the same cardinality (that of the real numbers) AND it is provable in ZFC.

The title is a little misleading, its really saying that two infinite sets are the same size, but prior to this their cardinality was unknown, and it wasn't even known if the cardinality was provable in ZFC.

This picture is for natural numbers but it shows you one way to do the mapping:

https://plus.maths.org/issue47/features/macgregor/diagram3.g...

The natural numbers are each finite. In set theory, the standard way they are defined is that they can be constructed by assuming the existence of the empty set (or 0) and assuming that if you "insert a set into itself" the result will be a set. (So they can be thought of as {} = 0, {{}} = 1, {{}, {{}}} = 2, etc.).

The natural numbers are simply the (smallest) set that contains the empty set and is closed under this "insert a set into itself" operation (successor). It only contains finite sets since the successor operation will never turn an finite set into an infinite set.

The existence of this set of ALL natural numbers (an infinite object) relies on an axiom, the axiom of infinity.

There is no transfinite natural number.

The LCBO doesn't negotiate. The vendors set their price, LCBO adds its automatic markup and thats it. Of course, they will only stock your product if people are buying it.

You're all looking at this from a dev perspective ... look at Slack's customer base.

Slack Enterprise is expensive for a messaging service, and one of their main selling points is support and reliability. When a huge customer reports a breaking bug they need to resolve it ASAP, turnaround time is probably the number-one priority.