user43221: Private key is 32-byte number.
Address (Hash) is 20-byte number.
Is it true that there is many Private keys that have the same 20-byte hash?
P.S. How to get Address from Private key:
Private key (32-byte number, random) --1--> 04+Public key (64-byte number, elliptic curve point) --2--> Hash, Address (20-byte number) --3--> Address string (Base58 string).

Elliptic curve point multiplication
SHA256, ripemd160
Hex converts to Base58


user38482: hmmm, a bit confusing, maybe I can add some clarification, that also helps  other readers. A 32b number or a 20b number doesn't seem to be an exact description. Bytes are abbreviated as capital "B", and bits are abbreviated as lower "b" (IEC 80000-13, IEEE 1541). A 32b privkey would be 4 Bytes, that is a bit too short :-) 
A Bitcoin privkey is 32 Bytes (which is a 256-bit number). A Bitcoin address is a string of 26-34 chars, to be more "human readable". It is derived from the priv key in the following way: 
privkey --> public key --> sha256 --> ripemd160 (here we actually have 20 Bytes) --> + network Byte --> double sha256 --> +chksum --> +Bytes reordering --> base58 encoding. This reads more complex than it actually is, a good overview here: http://gobittest.appspot.com/Address
So your last question is a bit tricky:

Is it true that there is many Private keys that have the same 20b hash
  (Address)?

Generally the idea of the hashing is, that you enter a string into the function, and it returns a fixed length output. If you change a single bit in this string, the result returns totally different. And as Pieter said, going from output to input is nearly impossible. So if you are asking:

if you can generate the same address (or public key) from different private keys? --> no (until today, there was no proof for it, but there are projects on the way to find "collisions")
if all priv keys generate (Bitcoin) addresses with the same length? --> no,  addresses have 26-34 Bytes length. 
if all priv keys generate the same length of pubkeys (and hashed 20Bytes long), from which then the Bitcoin address is generated? --> yes


user208: Yes, that is true.
However, to go from an address to any corresponding private key still requires an unfeasibly large amount of computing.

43221: <p><code>Private key</code> is 32-byte number.</p>

<p><code>Address (Hash)</code> is 20-byte number.</p>

<p>Is it true that there is many <code>Private keys</code> that have the same 20-byte hash?</p>

<p>P.S. How to get <code>Address</code> from <code>Private key</code>:</p>

<p><code>Private key</code> (32-byte number, random) --1--> <code>04</code>+<code>Public key</code> (64-byte number, elliptic curve point) --2--> <code>Hash, Address</code> (20-byte number) --3--> <code>Address</code> string (Base58 string).</p>

<ol>
<li>Elliptic curve point multiplication</li>
<li>SHA256, ripemd160</li>
<li>Hex converts to Base58</li>
</ol>
 38482: <p>hmmm, a bit confusing, maybe I can add some clarification, that also helps  other readers. A 32b number or a 20b number doesn't seem to be an exact description. Bytes are abbreviated as capital "B", and bits are abbreviated as lower "b" (IEC 80000-13, IEEE 1541). A 32b privkey would be 4 Bytes, that is a bit too short :-) </p>

<p>A Bitcoin privkey is 32 Bytes (which is a 256-bit number). A Bitcoin address is a string of 26-34 chars, to be more "human readable". It is derived from the priv key in the following way: </p>

<p>privkey --> public key --> sha256 --> ripemd160 (here we actually have 20 Bytes) --> + network Byte --> double sha256 --> +chksum --> +Bytes reordering --> base58 encoding. This reads more complex than it actually is, a good overview here: <code>http://gobittest.appspot.com/Address</code></p>

<p>So your last question is a bit tricky:</p>

<blockquote>
  <p>Is it true that there is many Private keys that have the same 20b hash
  (Address)?</p>
</blockquote>

<p>Generally the idea of the hashing is, that you enter a string into the function, and it returns a fixed length output. If you change a single bit in this string, the result returns totally different. And as Pieter said, going from output to input is nearly impossible. So if you are asking:</p>

<ul>
<li><p>if you can generate the same address (or public key) from different private keys? --> no (until today, there was no proof for it, but there are projects on the way to find "collisions")</p></li>
<li><p>if all priv keys generate (Bitcoin) addresses with the same length? --> no,  addresses have 26-34 Bytes length. </p></li>
<li><p>if all priv keys generate the same length of pubkeys (and hashed 20Bytes long), from which then the Bitcoin address is generated? --> yes</p></li>
</ul>
 208: <p>Yes, that is true.</p>

<p>However, to go from an address to any corresponding private key still requires an unfeasibly large amount of computing.</p>
