Proving that 2=1

Don’t believe me?

Let x = 1.

Then x² = x.

So x² – 1 = x -1.

Dividing both sides by x -1, we conclude that x + 1 = 1

That is, since x = 1, 2 = 1.

Courtesy of Augustus De Morgan.  Proving that math really does suck.

 

On The Topic of Love

When I was younger, still in high school, I had two friends that were dating.  They dated for a good amount of time, almost a year, and they seemed to have a pretty stable relationship.  However, they always had one problem that kept coming up ever-so-often…the guy never told his girlfriend that he loved her.  Upon first glance, it doesn’t seem like that big of an issue, but it was for the girlfriend.  It wasn’t a problem with him not saying it often enough, it was a problem with him never saying it all and refusing to do so.  Eventually, when the girl realized that he just wasn’t going to say it, she broke up with him.

At the time I was frankly befuddled by this situation.  I couldn’t understand why he couldn’t just tell the girl that he loved her and saved their relationship.  His refusals seemed crazy to me.  It was only years later that I finally understood why he hadn’t done it and began to really respect his decision.

Love is a word that may of us throw around too often and haphazardly.  I do acknowledge that their are different contexts and meanings of the word.  Of course I tell my family I love them, although probably not often enough.  I also often express my love for my friends, well at least some of them.  That is the kind of love that needs to be shared often and with a variety of people.  I’m not referring to that kind of love.  I am talking about actually being in love with someone.  We often tell our “significant others” that we love them, but do we really mean it?  Oftentimes not.  I haven’t loved every girl that I’ve dated.  I’ve liked them; I’ve cared about them, but that doesn’t mean I love them.  Love is something much deeper.  I believe that if you truly love someone, that love never really goes away.  It may be hard to find; it may be a long time since you’ve acknowledged it, but it’s always there somewhere.  Now, I’m not saying that you can only love one person.  I believe that is too idealistic.  I don’t believe there is just one person for everyone.  I don’t believe there is some kind of divine destiny between two lovers.  But I do believe that true love is a rare and unique caring for a person that never fades away.

I think we all know deep down in our hearts whether we truly love someone or not and I don’t think we should tell someone that we love them unless we really mean it.  My friend could have told his girlfriend he loved her, and sure, they would have kept on dating.  Yet that wouldn’t have changed the fact that he didn’t truly feel that way in his heart.  Maybe that love would have eventually developed; I believe that love can grow.  But what if it hadn’t?  The girl would have kept falling deeper and deeper in love, while his feelings would have remained unchanged.  Then my friend would have either had to continue living with the knowledge that he didn’t love the girl he was with or finally confront her and leave her more heartbroken than he ever could have originally.  Saying “I love you” when you don’t mean it is a short-term solution, but it will never solve the ultimate problem in your heart.  Maybe my friend wasn’t so crazy after all.