Zenonian cucumber paradox

This is marvellous. It might be my favourite post from the always excellent Angry People in Local Newspapers. A 'Salad enthusiast' discovers that half a cucumber costs more than half the cost of a whole cucumber.  Just head over to the page to savour the true glory of the story.

He's right too.  Here's the proof. A cucumber increases in value by 15 pence (just under a quarter of its original value) just by being divided in two.

Thinking about it made me wonder if there is a Zenonian axio-mereological paradox lurking here: If the value of a 'greenhouse-dwelling profusion' (another gem) increases the more the item is divided, then it should be possible to create a 'cylindrical garden favourite' (another - this reporter's on fire!) whose value tends to infinity just by continuing to divide each of the divisions.

And conversely, if each item in a multi-pack costs less the greater the number of such items in the multi-pack, then will the price of each item tend to zero as the number of items in the multi-pack increases? Should an infinity-pack therefore be free?