# 870: Advertising

## Explanation

This comic pokes fun at some advertising tricks, analyzing them mathematically.

- "Up to 15% or more" comes from Geico car insurance commercials: "15 minutes could save you up to 15% or more on car insurance." "Up to" means "less than or equal to," so the phrase means "less than, equal to, or more than 15%." Wait a second. All numbers are less than, equal to, or more than 15%! Thus the statement is a meaningless tautology.

- The first line uses notation from set theory and reads out as: The union of sets A and B equals the set of all x, such that x is less than or equal to 15, or greater than 15, which equals the set of all real numbers.
- Below is a number line (with the numbers being interpreted as percentages) the black dot indicates that the number 15 is included, and the white dot indicates that 15 is not included, but only strictly bigger numbers.

- Some things in life are free. However, typically not those aggressively advertised, with a capital "free!" splashed right over the ads, followed by a small asterisk, indicating the presence of a fine print, ensuring that they are only technically not guilty of false advertising. (Get a
**FREE*** drink!)

- The little formula Randall gives us, to calculate the least amount of money that they expect to make from you. The suggestion is that they expect their income from the ad to be more than what they paid for it. (*with the purchase of a $6 meal)

- Some sales are based on a scaling percentage rate - for example, all items are 20% off, but if you spend more than $200, you get 30% off instead, and so on. These are almost universally proclaimed with a phrase like "The more you spend, the more you save!" This is of course nonsense, as "spending" is the opposite of "saving", and the deal is there to make you spend more.

## Trivia

Randall changed the image name from advertising.png to mathematically_annoying.png, since adblocking extentions interpreted it as an ad and made the comic blank. He had had the same problem again just three months later with 906: Advertising Discovery.

## Transcript

- Mathematically Annoying Advertising:

- A ∪ B = {x:x ≤ 15 or x > 15} = ℝ
- [line graph representing the above equation.]
- When discussing real numbers, it is impossible to get more vague than "up to 15% or more".

- ["FREE!*" in large text, with substantial illegible fine print.]
- If someone has paid $x to have the word "free" typeset for you and N other people to read, their expected value for the money that will move from you to them is at least $(x / (N+1))

- [Graph representing inverse relationship between "amount you spend" on the y axis and "amount you save" on the x axis.]
- It would be difficult for the phrase "the more you spend the more you save" to be more wrong.

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# Discussion

But the Geico commercial doesn't say up to, it says 15% or more... ~Jfreund

- That may depend on your region. 108.162.216.30 03:24, 30 November 2013 (UTC)
- Saying that something "could save you 15% or more" and saying it "could save you
*up to*15% or more" are the same thing. Both statements take into account the very real possibility that some percentage less than 15 could be saved.Orazor (talk) 13:37, 21 July 2014 (UTC)

Not to mention that Geico says "**Could** save you..." (In combination with "up to", the "could" should be "will".) Z (talk) 03:09, 18 June 2014 (UTC)

A justification for "The more you buy, the more you save" is that the more discounted products you buy, the more money you save as opposed to buying them at list price. For things we will buy anyway (e.g. food), it may be true. --Troy0 (talk) 20:01, 6 July 2014 (UTC)

- Added to the article. --Troy0 (talk) 04:10, 25 July 2014 (UTC)
- It doesn't work when the items can expire. Cflare (talk) 14:38, 14 August 2014 (UTC)
- it does to a certain point- my family can eat a lot of food before it expires, especially if it's something we like. 108.162.237.163 (talk)
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- it does to a certain point- my family can eat a lot of food before it expires, especially if it's something we like. 108.162.237.163 (talk)

- It doesn't work when the items can expire. Cflare (talk) 14:38, 14 August 2014 (UTC)

Brilliant comic Randall. I wonder what your next one is about.

I used Google News BEFORE it was clickbait (talk) 00:20, 24 January 2015 (UTC)