I can make 1 + 1 = 1. What am I?

I begin with the last.

I can make 1 + 1 = 1.

If you miss me, then I will make you shy.

My other side can be used as identification.

I can make things smaller.

Sometimes I can upset you.

Can you guess me what am I?

• See also Riddle with a fang, which is probably utterly unrelated :-) – Rand al'Thor Oct 2 '16 at 11:24
• @rand al;thor Answer is different.. – KSR Oct 2 '16 at 11:31
• Yep, that's what I thought. Interesting how the same line can be used in two different riddles to mean two entirely different things (and can inspire people to create new kinds of puzzles)! – Rand al'Thor Oct 2 '16 at 11:33
• I think I may have the answer, but I'm having trouble making it fit with the 3rd, (4th), and 6th lines. – Rand al'Thor Oct 2 '16 at 13:33
• @rand al'thor please post partial answer... – KSR Oct 2 '16 at 14:19

Are you

ZIP

I begin with the last.

First letter is 'Z', the last letter of the alphabet.

I can make 1 + 1 = 1.

This is more or less what any fastening device does. In this case, examples could be a zipper, a .zip file, or the python zip function.

If you miss me, then I will make you shy.

If you forget to 'zip' your pants, you might become embarrassed.

My other side can be used as identification.

Zip codes

I can make things smaller.

File compression via .zip

Sometimes I can upset you.

Nothing solid for this one...

• A zip can upset if it does not work. – Anixx Oct 2 '16 at 17:28
• "identification" = zip code? – Rand al'Thor Oct 2 '16 at 17:51
• The expression "zip it" can upset people? dictionary.cambridge.org/dictionary/english/zip-it – Martijn Oct 2 '16 at 19:18
• @kayzeroshot Congrats!!! you are correct..upvote for you.. – KSR Oct 3 '16 at 2:47
• @kayzeroshort "Sometimes I upset you" See There's Something About Mary – Kevin Oct 3 '16 at 15:21

Took me a minute, but you are definitely

A pair of shoes

I begin with the last.

A pair of shoes can be made with a last -- Credit to @h34

I can make 1 + 1 = 1.

1 shoe + 1 shoe = 1 pair of shoes

If you miss me, then I will make you shy.

If you forget your shoes you will be shy

My other side can be used as identification.

footprints are used in investigations

I can make things smaller.

Stepping on things can make them smaller. Also the fact that they make you taller can make other things smaller.

Sometimes I can upset you.

Tripping on shoelaces can aggravate you.

• The making of shoes can begin using a last. – h34 Oct 2 '16 at 22:57
• @h34 Thanks, you strengthened my weakest point. I'm now pretty sure I got this right! Credited you in main post. – cheddar Oct 2 '16 at 23:25
• Nice..upvote for you.. – KSR Oct 3 '16 at 4:05
• Why would forgetting ones shoes make one "shy"? And you step on things with your feet, regardless of whether you are wearing shoes. Finally, avoid the word "definitely"... ;) – Lightness Races in Orbit Oct 3 '16 at 15:20

As requested by the OP, I'm posting this as an answer even though my explanations for the third and fourth lines are quite shaky.

ZERO.

I begin with the last.

The word "zero" begins with the last letter of the alphabet, Z.

I can make 1 + 1 = 1.

In binary, $1+1=10$ - the addition of a zero makes the equation 1+1=1 true.

If you miss me, then I will make you shy.

Missing a zero when writing down a large number could be a big blunder (potentially putting you out by a factor of 10), which might make you shy. (Thanks to @Sid for help with this line - it's shaky, but still better than just "not sure", which is what I had before.)

My other side can be used as identification.

The best explanation I can come up with for this line (and it's very shaky) is that ZERO backwards is OREZ, and ores might be used in identifying metal deposits.

I can make things smaller.

Adding extra zeros to a number like $0.1$, to turn it into $0.01$ or $0.0001$, does indeed make it smaller.

Sometimes I can upset you.

Having zero of something can be upsetting? Or, better, getting a mark of zero in a text or exam can certainly be upsetting (thanks @Pere).

• For the third line, Probably missing a zero from, say, 1,000,000? It would be a huge blunder? – Sid Oct 2 '16 at 14:27
• @Sid Shaky, but less so than my explanation for the fourth line. Added - thanks :-) – Rand al'Thor Oct 2 '16 at 14:30
• @rand al'thor you tried well, some statements matched. But it is not the answer. Upvote for well tried.. – KSR Oct 2 '16 at 14:34
• @Sathi Is it a word beginning with Z, or have I interpreted the first line completely wrong? (or don't you want to say yet?) – Rand al'Thor Oct 2 '16 at 14:39
• About a zero upsetting you, in countries where marks are given as numbers, the usual scale is 0-10 (instead of A-E) with 0 being the worst possible mark. A zero mark is likely to upset students - at least those to expected to pass. – Pere Oct 3 '16 at 11:14

I begin with the last.

mirror - reverses things front to back

I can make 1 + 1 = 1.

mirror - raid mirroring makes two copies one. two mirror copies are actually 1.

If you miss me, then I will make you shy.

mirror - if you forget to look at yourself in the mirror, you might go around being shy.

My other side can be used as identification.

mirror - recognize yourself.

I can make things smaller.

mirror - rear-view mirror.

Sometimes I can upset you.

mirror - don't like the way you look.

• Welcome to Puzzling! Could you edit this answer to add in an explanation as to why you think it is correct? Thanks! – Deusovi Oct 2 '16 at 19:45

I am a

mistake or an error

I begin with the last.

While correcting errors/mistakes people begin by seeing the end results and then working downwards towards the root.

I can make 1 + 1 = 1.

It's a mistake.

If you miss me, then I will make you shy.

Silly mistakes/goof ups can make people shy.

My other side can be used as identification.

Mistakes can be used to identify the qualities, state of mind of the person who made them.

I can make things smaller.

It can reduce a person's ego, numerically smaller etc

Sometimes I can upset you.

Quite obvious :)

• Well tried........ – KSR Oct 3 '16 at 9:10