Tariq on nostr

True:
6<2x<4 for all 3<x<2

False:
6<2x<4 for some 3<x<2

Why?

I can convince myself the first is vacuously true. But why is the second false?

#maths #logic

1❤️1

Greg Restall · 2w

nostr:nprofile1qy2hwumn8ghj7un9d3shjtnyd968gmewwp6kyqpq2z9n440ym56q58xmfja8d9xnf2d28m2gks23f3v6g8atjqtak4yqchjrcx The second is false because there is no x such that 3<x<2, since 3 is not less than 2, so, a fortiori, there is no x where 6<2x<4 and 3<x<2, i.e., it's not the case that 6<2x<4 for some ...