Yes, age is just a number but if it's a big number people make judgements about you! I agree with Jalima about people who volunteer the information, "I'm xx (years)!" with an eager look and then stand back hoping to be patronised! I don't lie about my age (I'm currently 65) but there's one area of my life where I refuse to discuss it and that's karate. I don't want to be patronised, "Gosh! You do well.....for your age!" Nor do I wish to be dismissed and ignored in favour of someone younger. (Of course, that's inevitable in any sport where competition is important but in normal, everyday training sessions, I pay the same training fee as anyone else.) This is another version of other people's, "I am what I am." If you must judge me, make it for what I can do (in karate) not what you expect I wouldn't/shouldn't/can't possibly be expected to be able to do (at my age!)
As for older men looking for younger women, that's happened since time immemorial! Many of them seem to see something in the mirror that's very different from what others see! One of our karate instructors was overheard saying he'd left his wife because he didn't want to live with an old woman. They were the same age as each other and he's no Adonis! He does have a new, very much younger wife, though. Women often see past the appearance of age in a man and are attracted by money and status. Traditionally, single, older women have had little money and no particular status. Hopefully, that's beginning to change.